
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
Circle $\Gamma$ is the circumcircle of $\triangle ABC$ and also serves as the incircle of $\triangle XYZ$. $X$, $Y$, and $Z$ lie on segments $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively. If $\angle A = 50^\circ$, $\angle B = 70^\circ$, and $\angle C = 60^\circ$, find the measure of $\angle YZX$.

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