
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 that three circles with centers at $P$, $Q$, and $R$ have radii of $2$, $3$, and $4$, respectively, and are tangent to the same line from below at points $P'$, $Q'$, and $R'$, respectively, and the circles centered at $P$ and $R$ are externally tangent to the circle centered at $Q$, determine the area of triangle $PQR$.

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