
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 of a convex quadrilateral are \(a\) and \(b\), and the line segments connecting the midpoints of opposite sides are equal to each other. Find the area of the quadrilateral.

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