
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 radius $6$ meters. Eight rectangular place mats are placed on the table. Each place mat has a width of $1.5$ meters and length $y$ meters. The mats are arranged so that each mat's two corners on one side touch the edge of the table, with these points being the endpoints of the side of length $y$. Moreover, each mat’s inner corners, which are orthogonal to the table’s edge, touch the inner corners of adjoining mats. Calculate the length $y$ of the place mats.
A) 3.75 meters
B) 3.9308 meters
C) 4.00 meters
D) 4.10 meters

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