Check Teamwork.com budgets against what the client pays in Rillet

**Objective:** Compare what `{company-name}` is contracted for in Rillet with the budgets its projects are delivering against in Teamwork, and flag where the two disagree.

**Step 1: Read the contracts in Rillet**

Find the customer: call `rillet-get-customers` and match `name` or `invoicing-name` to `{company-name}` (ignore case, punctuation and legal suffixes). If several match, list them and stop. Call `rillet-get-contracts` with that `customer-id`. Keep `name`, `status`, `start-date`, `end-date`, `total-value`, `currency` and `invoicing-interval`. Call `rillet-get-contract-items` with the same `customer-id` for the products on each contract.

**Step 2: Read the project budgets in Teamwork**

Call `teamwork-get-companies` with `name.contains` = `{company-name}` and then `teamwork-get-projects` with its `company-id`. If the company is not found by name, use `rillet-get-customer-emails` and `teamwork-get-people` to match by email domain. For each project, call `teamwork-get-budgets` with `project-id`. Keep `type`, `capacity`, `capacity-used`, `currency-code`, `start-date`, `end-date`, `is-retainer` and `status`.

**Step 3: Pair them**

Pair each Teamwork financial budget with the Rillet contract whose term overlaps the budget dates. Time budgets (hours) cannot be compared with contract value directly; convert them using `default-rate` when it is set, and say you did.

**Step 4: Report**

A table: contract, contract value and term, paired project and budget, budget capacity, used, percent used. Flag:
* budget capacity above contract value (the team is planning more than was sold);
* capacity used above contract value (work beyond what the client is paying for);
* an active contract with no budget, or a budget with no contract;
* a contract that has ended while its project is still active in Teamwork;
* term dates more than 30 days apart between contract and budget.

**Rules & Guidelines:**

* Tools starting teamwork- are on the teamwork MCP server; tools starting rillet- are on the rillet MCP server. If a tool from either server is unavailable, say which server is not connected and stop.
* This prompt is read-only. Do NOT call `rillet-add-invoice`, `rillet-update-invoice`, `rillet-add-customer`, `rillet-update-customer`, `rillet-add-credit-memo`, `teamwork-create-company`, `teamwork-update-company`, `teamwork-create-time-entry`, `teamwork-update-time-entry`, or any other tool on either server whose name starts with add, update, create, apply, set or record.
* Never convert between currencies. If Teamwork and Rillet amounts are in different currencies, report both side by side and say the comparison is not like for like. Teamwork's site currency is `currency-code` from `teamwork-get-account`.

**Validation:**

* If the customer has no contracts, say so and list the budgets only.
* If no project has a budget, say so and list the contracts only.