
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 heap of stones has a total weight of 100 kg, where the weight of each stone does not exceed 2 kg. Choose some stones from this heap in any combination and find the difference between the sum of these chosen stones' weights and 10 kg. Denote by $d$ the minimum value of the absolute value of these differences. Find the maximum value of $d$ among all heaps of stones satisfying the above conditions.

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