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

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