
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 placemats are placed on the table. Each placemat has width 1 unit and length y, arranged such that each placemat's longer edge lies along the edge of the table with its two corners touching the table's edge, and adjacent mats’ inner corners are touching one another. Calculate y.
A) \(5\sqrt{2 - \sqrt{2}}\)  
B) \(5\sqrt{2 + \sqrt{2}}\)  
C) \(7(\sqrt{2 - \sqrt{2}})\)  
D) \(4(\sqrt{2 + \sqrt{2}})\)

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