
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A pool is equipped with an inlet pipe and an outlet pipe. If only the inlet pipe is opened, it takes 2 hours and 20 minutes to fill the empty pool. Currently, the pool contains $\frac{1}{3}$ of its capacity in dirty water. When the outlet pipe is opened, it takes 1 hour and 20 minutes to drain all the dirty water. After draining the dirty water, the inlet pipe is opened, and after some time, it is discovered that the outlet pipe was not closed. When the outlet pipe is finally closed, the clean water in the pool has reached $\frac{1}{2}$ of the pool's capacity. The question is, how much time has passed from the moment the outlet pipe was opened until it was closed?

Present the answer in LaTex format: \boxed{Your answer}
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