
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 diagonal of a square is $2\sqrt{2}$ inches long. Directly next to it is another square whose diagonal is twice the length of the diagonal of the first square. Find the side length of both squares.

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