
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 height of a regular quadrilateral prism \( A B C D A_{1} B_{1} C_{1} D_{1} \) is twice as small as the side of its base. Find the maximum value of the angle \( \angle A_{1} M C_{1} \), where \( M \) is a point on edge \( AB \).

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