
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
Point \( M \) is the midpoint of side \( AB \) of triangle \( ABC \). Circle \(\omega_{1}\), which is tangent to line \( AC \), passes through points \( A \) and \( M \). Circle \(\omega_{2}\), which is tangent to line \( BC \), passes through points \( B \) and \( M \). The circles \(\omega_{1}\) and \(\omega_{2}\) intersect again at point \( D \). Point \( E \) lies inside triangle \( ABC \) and is symmetric to point \( D \) with respect to line \( AB \). Find the angle \( CEM \).

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