
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 \(ABC\), the median \(AM\) is drawn. Circle \(\gamma\) passes through point \(A\), is tangent to line \(BC\) at point \(M\), and intersects sides \(AB\) and \(AC\) at points \(D\) and \(E\) respectively. On the arc \(AD\) that does not contain \(E\), a point \(F\) is chosen such that \(\angle BFE = 72^\circ\). It is known that \(\angle DEF = \angle ABC\). Find the angle \(\angle CME\).

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