
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
On a sheet of graph paper, two rectangles are drawn. For the first rectangle, the vertical side is shorter than the horizontal side, and for the second rectangle, it's the opposite. Find the maximum possible area of their intersection if each rectangle contains more than 2010 but less than 2020 cells.

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