
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
A circle $\omega$ with center $O$ is circumscribed around triangle $ABC$. Circle $\omega_{1}$ is tangent to line $AB$ at point $A$ and passes through point $C$, and circle $\omega_{2}$ is tangent to line $AC$ at point $A$ and passes through point $B$. A line is drawn through point $A$ that intersects circle $\omega_{1}$ a second time at point $X$ and circle $\omega_{2}$ a second time at point $Y$. Point $M$ is the midpoint of segment $XY$. Find the angle $OMX$.

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