
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 diagonals \(AC\) and \(BD\) of the symmetric trapezoid \(ABCD\) intersect at point \(O\). The area of triangle \(AOB\) is \(52 \, \text{m}^2\) and the area of triangle \(COD\) is \(117 \, \text{m}^2\). Calculate the area of the trapezoid.

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