
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
Points \( E \) and \( F \) are chosen on the sides \( BC \) and \( CD \) of the square \( ABCD \) in such a way that the angle \( EAF \) is \( 45^\circ \). The side length of the square is 1. Find the perimeter of the triangle \( CEF \). Justify your solution.

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