
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 circular table with a radius of $5$ units, find the length $y$ of each rectangular place mat, where eight mats are positioned around the table with two corners of one of its long sides resting on the table's edge, and adjacent mats touching each other internally.

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