
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 of radius \( r \) is concentric with and outside a regular octagon of side length 3. The probability that three consecutive sides of the octagon are visible from a randomly chosen point on the circle is \( \frac{1}{2} \). What is \( r \)?
A) \( 10.76 \) 
B) \( 11.76 \)
C) \( 12.76 \)
D) \( 13.76 \)

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