
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
Two identically accurate clocks are hanging on the wall. One shows Moscow time, and the other shows local time. The minimum distance between the ends of their hour hands is $m$, and the maximum distance is $M$. Find the distance between the centers of these clocks.

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