
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
Let circle $\Theta$ be both the incircle of $\triangle DEF$ and the circumcircle of $\triangle PQR$. The point $P$ lies on $\overline{EF}$, point $Q$ on $\overline{DE}$, and point $R$ on $\overline{DF}$. Given $\angle D = 50^\circ$, $\angle E = 70^\circ$, and $\angle F = 60^\circ$, find the measure of the angle $\angle QRP$.

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