
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
Given a set of positive real numbers \(A=\left\{a_{1}, a_{2}, a_{3}, \cdots, a_{100}\right\}\), define the set \(S=\{(a, b) \mid a \in A, b \in A, a - b \in A\}\). Determine the maximum number of elements in the set \(S\).

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