
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
Early in the morning, a pump was turned on to start filling a pool. At 10 AM, an additional pump was switched on, and by 12 PM the pool was half full. At 5 PM, the pool was completely full. What is the latest possible time the first pump could have been turned on?

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