
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 round table has a radius of $5$ feet. Eight rectangular place mats are placed on the table, each with a width of $1$ foot and length $y$ feet. The mats are positioned so that the two corners of one width side touch the border of the table, and the inner corners of adjacent mats touch each other. Determine the length $y$ of each place mat.
A) $3.92$
B) $3.68$
C) $4.15$
D) $3.50$

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