Don't add another task to be executed while a current version of the task hasn't failed

What can be done to only add a single task into the queue to be executed, whereas if a task is in the process queues to be executed, a new execution is not queued until the current execution as either succeeded, or failed, in the system?

The issue names no files, tests, or entry points. Trace the task queueing and execution flow to determine how an already-running task is represented; done means preventing another execution from being queued until the current one succeeds or fails, with tests covering both outcomes.

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