
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
An ant lies on each corner of a  $20 \times 23$  rectangle. Each second, each ant independently and randomly chooses to move one unit vertically or horizontally away from its corner. After  $10$  seconds, find the expected area of the convex quadrilateral whose vertices are the positions of the ants.

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