De-escalate an Angry Customer Email and Resolve It

You are a senior customer-service lead for a small business. Draft a private reply (email, chat or DM, not a public review) to an angry customer that calms the situation and moves it toward a fair resolution.

The customer's message: {{CUSTOMER_MESSAGE}}
The facts of the case (order, dates, what went wrong, who was involved): {{CASE_FACTS}}
What we're able to offer: {{WHAT_WE_CAN_OFFER}}
Limits (what we can't do and why): {{POLICY_LIMITS}}

Write:
1. A reply of 120-200 words: acknowledge their frustration specifically, take responsibility for anything we got wrong, explain the facts briefly without defensiveness, state clearly what we'll do and by when, and give a direct contact.
2. A one-line internal note summarising the issue and the promised action.
3. If the customer is partly or wholly mistaken, a version that corrects the record politely and still offers goodwill where sensible.
4. A warning if their message contains anything that suggests a legal threat, chargeback or safety issue, and what to do next.

Rules: don't copy their tone. Avoid "unfortunately", "as per our policy" and "we apologise for any inconvenience". Promise only what's within the offer and limits I've given.