
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 $PQR$ has vertices $P = (4,0)$, $Q = (0,4)$, and $R$, where $R$ is on the line $x + y = 8$ and also on the line $y = 2x$. Find the area of $\triangle PQR$.
A) $\frac{4}{3}$
B) $\frac{6}{3}$
C) $\frac{8}{3}$
D) $\frac{10}{3}$
E) $\frac{12}{3}$

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