
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
A point \( E \) is taken on the base \( AB \) of an isosceles triangle \( ABC \), and the incircles of triangles \( ACE \) and \( ECB \) touch the segment \( CE \) at points \( M \) and \( N \) respectively. Find the length of the segment \( MN \), given the lengths of segments \( AE \) and \( BE \).

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