
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
Three circles with centers \( P, Q, \) and \( R \), have radii 2, 3, and 4 respectively. They lie on the same side of line \( l \) and are tangent to \( l \) at points \( P', Q', \) and \( R' \), respectively, with \( Q' \) between \( P' \) and \( R' \). The circle centered at \( Q \) is externally tangent to each of the other two circles. Determine the area of triangle \( PQR \).
- **A)** \( 1 \)
- **B)** \( \sqrt{2} \)
- **C)** \( \sqrt{3} \)
- **D)** \( 2 \)

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