
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 10 inches and 6 inches respectively. If the distance between the points of contact of the belt with the pulleys is 30 inches, determine the distance between the centers of the pulleys in inches.

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