
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 radius $5$. Five rectangular place mats are placed on the table. Each place mat has width $1$ and length $x$. These mats are positioned such that two corners of each mat touch the edge of the table on the same side length $x$, and the inner corners of each mat touch the inner corners of an adjacent mat, forming a regular pentagon in the center. Determine the value of $x$.
A) 1.5
B) 1.4
C) 1.3
D) 1.6

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