
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
An uncrossed belt is fitted without slack around two circular pulleys with radii of $12$ inches and $6$ inches. If the distance between the points of contact of the belt with the pulleys is $30$ inches, then the distance between the centers of the pulleys in inches is:
A) $2\sqrt{155}$
B) $2\sqrt{234}$
C) $2\sqrt{300}$
D) $34$

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