Add bank statement reconciliation to PDF processor prompt

- Add reconciliation check section to PdfProcessor instructions
- Extended JSON response to include reconciliation data
- Added reconciliation field to PdfProcessingResult Data.define

The LLM now uses available tools (GetAccounts, GetTransactions) to:
- Match statement to correct account
- Compare closing balance with account balance
- Compare transaction counts
- Match individual transactions (date ±1 day, amount ±sh.10)
- Report new and missing transactions

Fixes #1379

app/models/provider/llm_concept.rb

@@ -19,7 +19,7 @@ module Provider::LlmConcept
     raise NotImplementedError, "Subclasses must implement #enhance_provider_merchants"
   end
 
-  PdfProcessingResult = Data.define(:summary, :document_type, :extracted_data)
+  PdfProcessingResult = Data.define(:summary, :document_type, :extracted_data, :reconciliation)
 
   def supports_pdf_processing?
     false

app/models/provider/openai/pdf_processor.rb

@@ -63,6 +63,14 @@ class Provider::Openai::PdfProcessor
          - Opening and closing balances (if visible)
          - Currency used
 
+      4. **Reconciliation Check** (ONLY for bank_statement or credit_card_statement):
+         - First, use available tools to get accounts and their transactions for the relevant time period
+         - Match the statement to the correct account by comparing institution name, account holder, or account number
+         - Compare the statement closing balance with the account current balance
+         - Count transactions in the statement and compare with synced transaction count for that period
+         - Match individual transactions (by date within ±1 day, amount within ±$0.10, similar description)
+         - Report which transactions are new (in statement but not synced) and which are missing (synced but not in statement)
+
       IMPORTANT GUIDELINES:
       - Be factual and precise - only report what you can clearly see in the document
       - If information is unclear or redacted, note it as "not clearly visible" or "redacted"
@@ -84,6 +92,18 @@ class Provider::Openai::PdfProcessor
           "closing_balance": number or null,
           "currency": "USD/EUR/etc or null",
           "account_holder": "Name or null"
+        },
+        "reconciliation": {
+          "performed": true|false,
+          "account_id": "account_id or null",
+          "balance_match": true|false|null,
+          "statement_transaction_count": number|null,
+          "synced_transaction_count": number|null,
+          "matched_count": number|null,
+          "new_count": number|null,
+          "missing_count": number|null,
+          "new_transactions": [{"date":"YYYY-MM-DD","amount":0.00,"description":"..."}],
+          "missing_transactions": [{"date":"YYYY-MM-DD","amount":0.00,"description":"..."}]
         }
       }
     INSTRUCTIONS
@@ -226,7 +246,8 @@ class Provider::Openai::PdfProcessor
       PdfProcessingResult.new(
         summary: parsed["summary"],
         document_type: normalize_document_type(parsed["document_type"]),
-        extracted_data: parsed["extracted_data"] || {}
+        extracted_data: parsed["extracted_data"] || {},
+        reconciliation: parsed["reconciliation"]
       )
     end