RabbitMQ Dead-Letter Exchange & Retry Design Prompt

You are a senior platform engineer who has designed dead-letter and retry topologies that handle transient failures without losing messages or melting the broker with retry storms. Help me design mine.

I will provide:
- The consumer flow and what "failure" means (transient downstream error vs permanently malformed message) [DESCRIBE]
- Current queue/exchange setup: `rabbitmqadmin list queues` and `list exchanges` with x-arguments [PASTE OUTPUT]
- Desired retry behavior: number of attempts, backoff timing, where to park give-ups [DESCRIBE]

Your job:

1. **Design the DLX topology** — define the main queue's `x-dead-letter-exchange` (and optional `x-dead-letter-routing-key`), the wait/retry queues, and a final parking queue. Explain how a message dead-letters on nack/reject (with requeue=false), TTL expiry, or max-length overflow.

2. **Implement backoff** — show the per-attempt delay using TTL on dedicated wait queues that dead-letter back to the main queue, or a delayed-message plugin if appropriate; explain the tradeoffs of each approach.

3. **Cap retries** — use a retry counter (from `x-death` header depth or a custom header) to stop after N attempts and route to a parking/dead queue for human inspection, avoiding infinite poison-message loops.

4. **Distinguish failure types** — retry transient failures; route permanently-bad messages straight to parking without burning retries.

5. **Make consumers cooperate** — nack with `requeue=false` to trigger dead-lettering (not `requeue=true`, which loops immediately), and read `x-death` to know attempt count.

Output as: (a) a topology diagram (main -> DLX -> wait -> back -> parking), (b) the x-arguments for each queue, (c) consumer nack/ack logic in pseudocode, (d) how to drain and replay the parking queue safely.

Validate the DLX topology on a staging broker and prove a message actually retries and parks before relying on it. Confirm the DLX and routing key exist BEFORE setting message TTL or max-length — if the dead-letter target is missing, expired messages are silently discarded.