
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 a circle of radius  $r$  and a tangent line  $\ell$  to the circle through a given point  $P$  on the circle.  From a variable point  $R$  on the circle, a perpendicular  $RQ$  is drawn to  $\ell$  with  $Q$  on  $\ell$ .  Determine the maximum of the area of triangle  $PQR$ .

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