
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 area of trapezoid \(ABCD\) is 405. Diagonals intersect at point \(O\). The segments connecting the midpoint \(P\) of base \(AD\) with vertices \(B\) and \(C\) intersect the diagonals of the trapezoid at points \(M\) and \(N\). Find the area of triangle \(MON\), given that one of the bases of the trapezoid is twice as long as the other.

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