
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  $\triangle PQR$ , with  $PQ=PR=5$  and  $QR=6$ , is inscribed in circle  $\omega$ . Compute the radius of the circle with center on  $\overline{QR}$  which is tangent to both  $\omega$  and  $\overline{PQ}$ .

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