
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, without any slack, is fitted around two circular pulleys, with one having a radius of $10$ inches and the other $6$ inches. The distance between the points where the belt touches the pulleys is $26$ inches. What is the distance between the centers of the two pulleys in inches?
A) $2\sqrt{178}$
B) $2\sqrt{169}$
C) $2\sqrt{173}$
D) $2\sqrt{180}$

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