
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 rectangle measures 15 inches by 18 inches. Two circles, each with a diameter of 7.5 inches, are drawn so that each circle is tangent to one of the shorter sides and one of the longer sides of the rectangle. What is the greatest possible distance between the centers of these two circles?

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