
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 set  $D$  of positive integers is called *indifferent* if there are at least two integers in the set, and for any two distinct elements  $x,y\in D$ , their positive difference  $|x-y|$  is also in  $D$ . Let  $M(x)$  be the smallest size of an indifferent set whose largest element is  $x$ . Compute the sum  $M(2)+M(3)+\dots+M(100)$ .

*Proposed by Yannick Yao*

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