
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  $\omega$  and  $\Gamma$  be circles such that  $\omega$  is internally tangent to  $\Gamma$  at a point  $P$ . Let  $AB$  be a chord of  $\Gamma$  tangent to  $\omega$  at a point  $Q$ . Let  $R\neq P$  be the second intersection of line  $PQ$  with  $\Gamma$ . If the radius of  $\Gamma$  is  $17$ , the radius of  $\omega$  is  $7$ , and  $\frac{AQ}{BQ}=3$ , find the circumradius of triangle  $AQR$ .

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