
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
Suppose Harvard Yard is a \( 17 \times 17 \) square. There are 14 dorms located on the perimeter of the Yard. If \( s \) is the minimum distance between two dorms, the maximum possible value of \( s \) can be expressed as \( a-\sqrt{b} \) where \( a \) and \( b \) are positive integers. Compute \( 100a + b \).

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