
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
Fido's leash is tied to a stake at the center of his yard, which is shaped as a regular octagon. His leash length allows him to reach the midpoint of each side of the yard. If the fraction of the area of Fido's yard that he can reach while on his leash is expressed in its simplest radical form as $\frac{\sqrt{a}}{b}\pi$, determine the value of the product $ab$.

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