
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
A circular table has a radius of 6 units, and eight rectangular place mats are placed on it. Each place mat has a width of 1 unit and a length such that two corners of the width side reside on the table's edge, while the inner corners of each mat precisely touch the inner corners of an adjacent mat. Determine the value of y.

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