
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
The hour and minute hands of a clock move continuously and at constant speeds. A time moment $X$ is called interesting if there exists a moment $Y$ (the moments $X$ and $Y$ do not necessarily have to be different) such that the hour hand at moment $Y$ will be at the same position as the minute hand at moment $X$, and the minute hand at moment $Y$ will be at the same position as the hour hand at moment $X$. How many interesting moments will there be from 00:01 to $12:01$?

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