
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
Given an isosceles triangle $PQR$ where $PR = QR$ and side $PQ$ is longer than $PR$, a circle with a radius equal to half the altitude of triangle $PQR$ from vertex $P$ rolls along side $PQ$, remaining tangent to it at a variable point $T$ and intersects lines $PR$ and $QR$ in variable points $M$ and $N$, respectively. Determine the expression that gives the number of degrees in arc $MTN$ for all permissible positions of the circle.

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