
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 \( ABC \), median \( AM \) is drawn. Circle \(\omega\) passes through point \( A \), touches line \( BC \) at point \( M \), and intersects sides \( AB \) and \( AC \) at points \( D \) and \( E \) respectively. On arc \( AD \), not containing point \( E \), a point \( F \) is chosen such that \(\angle BFE = 72^{\circ}\). It turns out that \(\angle DEF = \angle ABC\). Find the angle \(\angle CME\).

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