
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 the set $A=\{a_1, a_2, a_3, \ldots, a_n\}$ ($n\in\mathbb{N}^*$, $n\geq3$), define the capacity of the sum of two elements in set $A$ as the number of distinct values of $a_i+a_j$ ($1\leq i<j\leq n$, $i,j\in\mathbb{N}^*$). Denote this capacity as $L(A)$. If the sequence $\{a_n\}$ is an arithmetic sequence with a non-zero common difference, and the set $A=\{a_1, a_2, a_3, \ldots, a_{2016}\}$, then $L(A)=$ ?

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