
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. Eight rectangular place mats are placed on it. Each place mat has width $1$ unit and length $x$ units, with each mat having two corners on the table's edge and its inner corners just touching its adjacent mats. What is the correct length, $x$, of each place mat?
A) 3.5  
B) 3.82  
C) 4  
D) 4.22  
E) 4.5

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