
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 right triangle $\triangle PQR$ has side lengths $3$ (for $PQ$), $4$ (for $QR$), and $5$ (for $PR$). $S$ is the midpoint of $\overline{PQ}$, and $R$ is the midpoint of $\overline{TX}$, where $T$ is a point on $PQ$ such that $PT = 3$. Determine the area of $\triangle TSR$.

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