
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 $5$ meters. Eight square place mats are arranged on the table so that two corners of each mat touch the circumference of the table, being endpoints of the same side. The sides of the mats lying on the table are further aligned such that inner corners of the mats touch inner corners of adjacent mats. If each place mat has a side length $x$, find the value of $x$.
A) $5\sqrt{2 - \sqrt{2}}$
B) $5\sqrt{2\sqrt{2}}$
C) $10\sqrt{2}$
D) $5\sqrt{2}$

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