
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 5 units. Five rectangular placemats are placed on the table such that each mat has a width of 1 unit and a length \( y \). Each placemat has two corners on the edge of the table, both endpoints of the width. The mats are positioned so that each inner corner touches an inner corner of an adjacent mat. Determine the value of \( y \).

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