
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
In \(\triangle XYZ\), let \(A\) be a point on the segment \(YZ\) such that \(XA\) is perpendicular to \(YZ\). Let \(M\) and \(N\) be the incenters of triangles \(XYA\) and \(XZA\), respectively. If \(YZ = 28\), \(XA = 24\), and \(YA = 10\), what is the length of \(MN\)?

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