
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
The diagram shows a triangle \(ABC\) with an area of \(12 \, \text{cm}^2\). The sides of the triangle are extended to points \(P, Q, R, S, T\) and \(U\) so that \(PA = AB = BS\), \(QA = AC = CT\), and \(RB = BC = CU\). What is the area (in \(\text{cm}^2\)) of hexagon \(PQRSTU\)?

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