
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
Given a round table with a radius of 5 and seven rectangular place mats with a width of 1 and an unknown length y, where each mat's inner corners touch the inner corners of adjacent mats, determine the length y.

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