
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
For the set $A=\left\{a_1,a_2,\ldots,a_n\right\} \left(n\in\mathbb{N}^*,n\geqslant 3\right)$, define the set $S=\left\{ x \mid x=a_i+a_j,1\leqslant i\leqslant j\leqslant n\right\}$. Let the number of elements in set $S$ be denoted as $S(A)$. If $a_1,a_2,\ldots,a_n$ form an arithmetic sequence with a positive common difference, then $S(A) =$\_\_\_\_\_\_\_\_\_\_\_\_.

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