Find Teamwork.com clients being served but never billed in Rillet

**Objective:** Reconcile the client list between Teamwork and Rillet, limited to companies whose name contains `{company-name-contains}` (default: every company), and report matches, gaps and differences.

**Step 1: Read the Teamwork companies**

Call `teamwork-get-companies`, passing `{company-name-contains}` as `name.contains` when it is given. Keep `company-id`, `name`, `email`, `website`, `city`, `state`, `zip`, `country-code` and `project-count`.

**Step 2: Read the Rillet customers**

Call `rillet-get-customers` (no filters; it returns every customer) and `rillet-get-customer-emails`. When `{company-name-contains}` is given, keep only customers whose `name` or `invoicing-name` contains it, ignoring case.

**Step 3: Match**

Match on name first, ignoring case, punctuation and legal suffixes (Inc, LLC, Ltd, Corp, GmbH). For companies left unmatched, call `teamwork-get-people` with the company's `company-id` and match a contact `email` against `rillet-get-customer-emails`, by exact address or shared company domain (never a public domain such as gmail.com). Do not match on city or state alone.

**Step 4: Report**

Four sections:
1. Matched: Teamwork name, Rillet name, match rule, and any differences in city, state, zip or country.
2. In Teamwork only: name, `project-count`. Put companies with projects first; these may be clients that are never invoiced.
3. In Rillet only: name, `customer-id`, `payment-terms`.
4. Ambiguous: any record that matched more than one record on the other side, with the candidates.

Finish with the counts for each section.

**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.
* Teamwork's own company (the site owner) usually appears in `teamwork-get-companies`; leave it out of the Teamwork-only list and say you did.

**Validation:**

* If either system returns no records, say which one and stop rather than reporting everything as unmatched.
* Country may be a code on one side and a name on the other; treat US and United States as the same.