
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 $\triangle PQR$ has an area of $20$ square units. Points $S, T, U$, distinct from $P, Q, R$, lie on sides $PQ, QR$, and $RP$ respectively, with $PS = 3$ and $SQ = 2$. If the triangle $\triangle PTQ$ and the quadrilateral $SQTR$ have equal areas, determine that area.
A) \( 6 \) square units
B) \( 8 \) square units
C) \( 10 \) square units
D) \( 12 \) square units
E) \( 14 \) square units

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