
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 angle bisector of angle \(B A C\) of triangle \(A B C\), a point \(M\) is marked, and on the extension of side \(A B\) beyond point \(A\), a point \(N\) is marked such that \(A C = A M = 1\) and \(\angle A N M = \angle C N M\). Find the length of segment \(A N\).

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