
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
Two square napkins with dimensions \(1 \times 1\) and \(2 \times 2\) are placed on a table so that the corner of the larger napkin falls into the center of the smaller napkin. What is the maximum area of the table that the napkins can cover?

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