
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
This week's math puzzle from the magazine "Modern Values" was particularly challenging. As I began thinking about it (between 9 and 10 o'clock), I noticed that the two hands of my clock formed a straight line, extending one from the other. I found the solution only at the moment when the hands overlapped with each other.

How long did my contemplation last?

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