
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 units. Eight rectangular place mats are placed on the table. Each place mat has width 1 unit and length \( x \). They are positioned such that each mat has two corners touching the edge of the table, and the mats are arranged so that the inner corners of each mat touch an inner corner of an adjacent mat. Determine the length \( x \) of each place mat's side that lies along the edge of the table.

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