
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 90. The diagonals intersect at point $O$. Segments connecting the midpoint $P$ of the base $AD$ with vertices $B$ and $C$ intersect with the diagonals of the trapezoid at points $M$ and $N$. Find the area of quadrilateral $OMPN$ if 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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