
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 belt is placed without slack around two non-crossing circular pulleys which have radii of $15$ inches and $5$ inches respectively. The distance between the points where the belt contacts the pulleys is $30$ inches. Determine the distance between the centers of the two pulleys.
A) $20$ inches
B) $10\sqrt{10}$ inches
C) $40$ inches
D) $50$ inches

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