
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 is concentric with and outside a regular hexagon of side length $3$. What should the radius of the circle be so that the probability a randomly chosen point on the circle will completely see exactly four sides of the hexagon is $\frac{1}{3}$?
A) $\frac{3}{4}$
B) $\frac{9}{4}$
C) $\frac{3}{2}$
D) $3$

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