Let me start by listing documents and looking up references. Actually, I need to first list documents to find the case inputs, then read them. The lookup_reference calls are independent of the documents, but I should first know the payroll month before selecting first-half or second-half. However, I can call list_documents first, and possibly lookup both halves? The instructions say to make independent calls in the same block. list_documents is independent. lookup_reference depends on knowing the month, so I should wait.

Let me call list_documents first.

Payroll month 2026-04, which is in the second half (April... need to check period boundaries). Let me look up second-half reference.

The second-half schedule returned months ["2026-07", "2026-12"]. That doesn't include 2026-04. Hmm, that's odd. Let me check first-half too — maybe the first-half covers other months. The lookup_reference tool returns first-half or second-half payroll reference rates and effective months. Let me look up first-half.

The first-half covers months 2026-01 through 2026-06 (the "months" list shows the boundary months, presumably inclusive ranges: first-half = Jan–Jun, second-half = Jul–Dec). So 2026-04 falls in the first half: rate 0.07, cap 4500.00, deduction 400.00, free 1000.00, upper 3600.00, middle_rate 0.08, upper_rate 0.24.

Now calculate:
- gross_pay = 2107.50
- employee_contribution = round(min(4500.00, 2107.50) * 0.07, 2) = round(147.525, 2). Round half up: 147.525 → 147.53? 147.525 rounds half-up to 147.53. Let me verify with the calculator.
- allowed_deduction = 273.91. Check: must not exceed deduction cap 400.00, and not exceed gross pay minus rounded contribution = 2107.50 - 147.53 = 1959.97. 273.91 ≤ both. OK.
- taxable_pay = 2107.50 - 147.53 - 273.91 = 686.06.
- income tax: free = 1000.00. Taxable pay 686.06 ≤ 1000 → tax = 0.00.
- net_pay = 2107.50 - 147.53 - 273.91 - 0.00 = 686.06.

Let me use the calculate tool for exact arithmetic.

Wait — I made an error. taxable = 2107.50 - 147.53 - 273.91. Let me recompute: 2107.50 - 147.53 = 1959.97; 1959.97 - 273.91 = 1686.06. I earlier said 686.06 — that was wrong. Let me redo: 1959.97 - 273.91: 1959.97 - 273.91 = 1686.06. Yes, 1686.06.

So taxable pay = 1686.06, which is above the free amount of 1000.00 and below upper boundary 3600.00.

Tax = (1686.06 - 1000.00) * 0.08 = 686.06 * 0.08 = 54.8848 → round half up to 54.88. The calculator returned 54.88. Wait, 54.8848 rounds to 54.88 (since 54.8848 → two decimals: third decimal is 4, so 54.88). Correct.

But wait — my tax formula: (taxable - 1000) * 0.08 + max(0, taxable - 3600) * (0.24 - 0.08). Since taxable - 3600 = negative, max gives 0. So tax = 54.8848 → 54.88. Correct per R5: portion above free up to upper uses middle rate; portion above upper uses upper rate. Marginal: (1686.06 - 1000) * 0.08 = 54.8848. Round to 54.88.

Net pay = 2107.50 - 147.53 - 273.91 - 54.88 = 631.18? Let me compute: 2107.50 - 147.53 = 1959.97; 1959.97 - 273.91 = 1686.06; 1686.06 - 54.88 = 1631.18. The calculator says 1631.18. Good.

Hmm, but the calculator's net used the rounded tax (54.88), consistent with R6.

Wait — the calculator returned net = "1631.18". Let me verify: 1686.06 - 54.88 = 1631.18. Yes.

Now check allowed deduction validity: 273.91 ≤ 400.00 (cap) and ≤ 1959.97 (gross minus contribution). Valid.

Employee contribution: min(2107.50, 4500.00) = 2107.50 * 0.07 = 147.525 → round half up → 147.53. The calculator returned 147.53. Good.

The reference row: first-half months ["2026-01", "2026-06"] — I interpret this as the range 2026-01 through 2026-06. April 2026 falls within. The second-half covers 2026-07 through 2026-12. So 2026-04 uses first-half row.

Final answer fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "2107.50"
- employee_contribution: "147.53"
- allowed_deduction: "273.91"
- taxable_pay: "1686.06"
- income_tax: "54.88"
- net_pay: "1631.18"
- clauses: R1, R2, R3, R4, R5, R6
- explanation optional.

Let me start by listing the documents and looking up the reference tables. Actually, I need to first read the documents to know the payroll month, then look up the reference. But I can do list_documents and lookup_reference for both halves in parallel? The instructions say reference rows are available only through lookup_reference. I can fetch both first-half and second-half in parallel since they're independent. But which half applies depends on the month — I don't know the month yet. Let me first list documents, then read, then lookup the right half.

Let me call list_documents first.

Payroll month 2026-04. April is in the first half of the year (Jan–Jun presumably). Let me look up the first-half reference.

The reference row for 2026-04 (first half, months 2026-01 through 2026-06): rate 0.07, cap 4500.00, deduction cap 400.00, free 1000.00, upper 3600.00, middle_rate 0.08, upper_rate 0.24.

Inputs:
- gross_pay = 2107.50
- payroll_month = 2026-04 (covered)
- allowed_deduction = 273.91

Checks:
1. gross_pay present ✓
2. payroll_month present ✓
3. Reference row exists ✓
4. No contract_gross_pay, no amendment ✓

R3: employee contribution = 0.07 * min(2107.50, 4500.00) = 0.07 * 2107.50 = 147.525 → round half up to 147.53? Wait, 147.525 rounds half-up to 147.53. Let me compute: 2107.50 * 0.07 = 147.525. Round to two decimals, half up: 147.53.

Hmm, but let me double check: 2107.50 * 0.07 = 147.5250. Yes, 147.53.

R4: allowed_deduction = 273.91. Must not exceed deduction cap 400.00, nor gross pay minus rounded contribution = 2107.50 - 147.53 = 1959.97. 273.91 ≤ both. OK.

taxable_pay = 2107.50 - 147.53 - 273.91 = 686.06.

R5: taxable pay 686.06 ≤ free 1000.00, so tax = 0.00.

R6: net pay = 2107.50 - 147.53 - 273.91 - 0.00 = 686.06.

Let me verify with calculate.

Wait, the calculator returned taxable = 1686.06? Let me recompute: 2107.50 - 147.53 - 273.91.

2107.50 - 147.53 = 1959.97. 1959.97 - 273.91 = 1686.06. Hmm, I made an arithmetic error earlier. 1959.97 - 273.91: 1959.97 - 273.91 = 1686.06. Yes, I mis-subtracted before (I said 686.06). The calculator is right: taxable = 1686.06.

So taxable pay = 1686.06. That's above free 1000.00, so tax applies!

Portion up to 1000.00 untaxed. Portion above 1000.00 up to upper boundary 3600.00 uses middle rate 0.08. Taxable 1686.06 is below 3600, so entire excess 686.06 taxed at 0.08.

tax = 686.06 * 0.08 = 54.8848 → round half up = 54.88.

Let me redo the calculation properly.

Verification:
- contribution = 0.07 * 2107.50 = 147.525 → 147.53 (round half up). ✓
- deduction 273.91 ≤ cap 400.00 and ≤ 2107.50 - 147.53 = 1959.97. ✓
- taxable = 2107.50 - 147.53 - 273.91 = 1686.06. ✓
- tax: free 1000.00; excess 686.06 at middle rate 0.08 (since 1686.06 ≤ 3600.00 upper boundary) = 54.8848 → 54.88. ✓
- net = 2107.50 - 147.53 - 273.91 - 54.88 = 1631.18. ✓

Output JSON with decision calculate, currency LCR, fields as two-decimal strings, clauses R1–R6 (no amendment needed, so no R9). Include optional explanation.

Let me start by listing the documents to see what case inputs exist.

Let me read the payroll document.

The payroll record:
- gross_pay: 2107.50
- payroll_month: 2026-04
- allowed_deduction: 273.91

2026-04 is in 2026, so covered. April is in the first half of the year presumably (first-half reference). Let me look up the first-half reference.

First-half reference (months 2026-01 through 2026-06):
- rate: 0.07
- cap: 4500.00
- deduction cap: 400.00
- free: 1000.00
- upper: 3600.00
- middle_rate: 0.08
- upper_rate: 0.24

Payroll month 2026-04 is covered by the first-half row.

Now compute:
1. Employee contribution (R3): rate * min(gross, cap) = 0.07 * min(2107.50, 4500.00) = 0.07 * 2107.50 = 147.525 → round half up to 147.53.

Wait — R2 says round monetary calculation results to two decimal places using round-half-up. The contribution is a monetary calculation result, so round to 147.53.

2. Allowed deduction check (R4): allowed_deduction = 273.91. Must not exceed deduction cap (400.00) or gross pay minus rounded employee contribution (2107.50 - 147.53 = 1959.97). 273.91 ≤ 400.00 and ≤ 1959.97. Valid.

3. Taxable pay (R4): gross - contribution - allowed_deduction = 2107.50 - 147.53 - 273.91 = 686.06.

4. Income tax (R5): taxable pay 686.06 ≤ free (1000.00), so tax = 0.00.

5. Net pay (R6): gross - contribution - deduction - tax = 2107.50 - 147.53 - 273.91 - 0.00 = 686.06.

Let me verify with the calculator.

Wait, the calculator results look off. Let me check:

contribution = round(min(4500.00, 2107.50) * 0.07, 2) = round(2107.50 * 0.07, 2) = round(147.525, 2) = 147.53 (half up). OK.

available = 2107.50 - 147.53 = 1959.97. OK.

taxable = 2107.50 - 147.53 - 273.91. Let me compute: 2107.50 - 147.53 = 1959.97; 1959.97 - 273.91 = 1686.06. Hmm, I made an arithmetic error earlier: 1959.97 - 273.91 = 1686.06, not 686.06. Yes, 1959.97 - 273.91 = 1686.06. Correct.

tax = max(0, taxable - 1000.00) = max(0, 1686.06 - 1000.00) = 686.06. So taxable pay 1686.06 exceeds the free amount of 1000.00.

Now tax: taxable up to 1000.00 untaxed; portion above 1000.00 up to upper (3600.00) uses middle rate 0.08; portion above 3600.00 uses upper rate 0.24.

Taxable = 1686.06. Portion above free = 1686.06 - 1000.00 = 686.06, which is ≤ upper boundary 3600.00, so all taxed at middle rate 0.08: 686.06 * 0.08 = 54.8848 → round to 54.88.

My calculator program only computed taxable - free, not the actual tax. I need to redo the tax calculation properly.

net = 2107.50 - 147.53 - 273.91 - tax.

Let me compute the tax properly:
- bracket1 portion: min(taxable, free) → untaxed
- middle portion: max(0, min(taxable, upper) - free) * middle_rate
- upper portion: max(0, taxable - upper) * upper_rate

tax = middle portion + upper portion = 686.06 * 0.08 = 54.8848 → 54.88.

net = 2107.50 - 147.53 - 273.91 - 54.88 = 631.18.

Let me verify: 2107.50 - 147.53 = 1959.97; 1959.97 - 273.91 = 1686.06; 1686.06 - 54.88 = 1631.18. Wait: 1686.06 - 54.88 = 1631.18. Hmm, let me recompute: 1686.06 - 54.88 = 1631.18. Yes.

Wait, I said 631.18 before — that was wrong. 1686.06 - 54.88: 1686.06 - 50 = 1636.06; 1636.06 - 4.88 = 1631.18. Yes, net = 1631.18.

Let me run the calculator again with the correct bracket logic.

Results:
- contribution: 147.53
- taxable: 1686.06
- tax: 54.88 (middle portion 686.06 × 0.08 = 54.8848 → 54.88)
- net: 1631.18

Checks:
- R7 order: gross_pay present, payroll_month present (2026-04), reference row exists (first-half covers 2026-01..2026-06), no contract_gross_pay or amendment present. No clarification needed.
- R4: allowed_deduction 273.91 ≤ deduction cap 400.00 and ≤ available (2107.50 - 147.53 = 1959.97). Valid.
- R3: contribution = 0.07 × min(2107.50, 4500.00) = 147.525 → 147.53 (half-up).
- R5: taxable 1686.06; first 1000.00 untaxed; 686.06 at 0.08 = 54.8848 → 54.88.
- R6: net = 2107.50 - 147.53 - 273.91 - 54.88 = 1631.18.

Answer JSON with decision: calculate, currency LCR, fields as two-decimal strings, clauses R1, R2, R3, R4, R5, R6.