
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
$\triangle PQR$ is inscribed in a semicircle of radius $R$ so that its base $PQ$ coincides with the diameter $PQ$. Point $R$ does not coincide with either $P$ or $Q$. Let $t = PR + RQ$. Find the maximum possible value of $t^2$.

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