
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
Consider a standard twelve-hour clock whose hour and minute hands move continuously. Let  $m$  be an integer, with  $1 \leq m \leq 720$ . At precisely  $m$  minutes after 12:00, the angle made by the hour hand and minute hand is exactly  $1^\circ$ .
Determine all possible values of  $m$ .

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