
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 circle with radius \( r \) is concentric with and outside a regular octagon of side length \( 3 \). Calculate \( r \) such that the probability that four entire sides of the octagon are visible from a randomly chosen point on the circle is \( \frac{1}{3} \).
A) 3.5
B) 3.6
C) 3.7
D) 3.8

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