
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 $\omega_{1}$ passes through points $A$ and $M$ and is tangent to line $AC$, while circle $\omega_{2}$ passes through points $B$ and $M$ and is tangent to line $BC$. 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}
user