
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 $ABC$, on the midline $DE$ parallel to $AB$, a circle is constructed with $DE$ as the diameter, intersecting the extensions of sides $AC$ and $BC$ at points $M$ and $N$. Find $MN$ if $BC = a$, $AC = b$, and $AB = c$.

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