A third party API you depend on starts timing out intermittently. What do you do?

Contain it first: set an aggressive timeout so their latency does not become yours, retry with exponential backoff and jitter on idempotent calls only, and put a circuit breaker in front so you stop hammering something that is already down. Then decide what degraded behavior looks like: queue the work for later, serve a cached value, or fail that one feature while the rest of the product keeps working.

The first thing I check is whether we even have a timeout, because the default in a lot of HTTP clients is effectively forever, and that is how one slow provider fills your worker pool and takes down endpoints that have nothing to do with them. So an aggressive timeout, tighter than my own SLA. Then retries, but only on calls that are safe to repeat, with exponential backoff and jitter, because synchronized retries from every instance turn their brownout into a full outage. A circuit breaker goes in front, so after a run of failures we stop calling for a while and fail fast rather than queueing. Then the product question, which is the interesting one: what should the user see? For an address validation call I would let the order through and flag it for review. For a payment authorization I cannot fake it, so I queue the attempt and tell the user honestly. And I would be on their support channel with request ids the whole time.