
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
There were 99 numbers written on a board, all of which were distinct. In a notebook, $\frac{99 \cdot 98}{2}$ numbers were written down—all the differences between two numbers from the board (each time subtracting the smaller number from the larger one). It turned out that the number 1 appeared in the notebook exactly 85 times. Let $d$ be the largest number written in the notebook. Find the smallest possible value of $d$.

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