
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
Alice starts a trip when the hands of the clock are exactly $180^\circ$ apart between 11 a.m. and 12 p.m. She arrives at her destination when the hands of the clock are together between 4 p.m. and 5 p.m. Calculate the duration of the trip.

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