
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
Let $M = \{a_1, a_2, \ldots, a_n\}$ be a set composed of distinct positive integers $a_1, a_2, \ldots, a_n$ ($n \geq 2$, $n \in \mathbb{N}^+$). Define the set $S = \{(a, b) \mid a \in M, b \in M, a-b \in M\}$.
1. If $M = \{1,2,3,4\}$, then the set $S$ has at most \_\_\_\_\_\_ elements.
2. If $M = \{a_1, a_2, \ldots, a_n\}$, then the set $S$ has at most \_\_\_\_\_\_ elements.

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