
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

Martians divide their day into 13 hours. After the Martian Hare dropped the clock into tea, the speed of the second hand's rotation changed, while the speed of the other hands remained the same. It is known that every midnight all three hands align. How many moments in total during a day can these three hands coincide?

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