
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
In a 15-inch by 18-inch rectangle, two circles are drawn, each with a diameter of 7 inches. If the circles are positioned such that they do not extend beyond the rectangular boundaries, what is the greatest possible distance between the centers of the two circles?

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