
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
In the diagram, \(OAB\) is a triangle with \(\angle AOB = 90^\circ\) and \(OB = 13 \text{ cm}\). \(P\) and \(Q\) are two points on \(AB\) such that \(26AP = 22PQ = 11QB\). If the vertical height from \(P\) to \(Q\) is \(4 \text{ cm}\), find the area of the triangle \(OPQ\) in \(\text{cm}^2\).

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