
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 base $AB$ of an isosceles triangle $ABC$, a point $E$ is taken, and circles are inscribed in the triangles $ACE$ and $ECB$, touching the segment $CE$ at points $M$ and $N$. Find the length of the segment $MN$, given the lengths of the segments $AE$ and $BE$.

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