
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 $5$. Four rectangular place mats are placed on the table. Each place mat has width $1.5$ and length $y$. They are positioned such that two corners of each mat (on the same side) touch the edge of the table, and the inner corners of each mat touch the inner corners of adjacent mats. Calculate the value of $y$.

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