
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
Triangle $\triangle ABC$ has an excircle $\Omega$ and an incircle $\Gamma$. Circle $\Omega$ is also the circumcircle of $\triangle XYZ$. Point $X$ is on $\overline{BC}$, $Y$ is on $\overline{AB}$, and $Z$ is on $\overline{CA}$. If $\angle A = 50^\circ$, $\angle B = 70^\circ$, and $\angle C = 60^\circ$, determine the measure of $\angle XYZ$.

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