
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
In $\triangle PQR$, $S$ is the midpoint of side $QR$ and $T$ is on side $PR$. If the length of $PR$ is $12$ units and $\angle QPR = 45^\circ, \angle PQR = 90^\circ, \angle PRQ = 45^\circ$ and $\angle RTS = 45^\circ$, find the area of $\triangle PQR$ plus twice the area of $\triangle RST$.

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