
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
On the sides \( CB \) and \( CD \) of the square \( ABCD \), points \( M \) and \( K \) are taken such that the perimeter of the triangle \( CMK \) is equal to twice the side of the square.

Find the measure of angle \( MAK \).

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