
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 $A = \{a_1, a_2, a_3, \ldots, a_n\}$ ($n \in \mathbb{N}^*$, $n \geq 3$), define the capacity of the sum of two elements from set A, denoted as $L(A)$, to be the number of different values in $a_i + a_j$ ($1 \leq i < j \leq n$, $i, j \in \mathbb{N}^*$). If $A = \{2, 4, 6, 8\}$, then $L(A) =$ ______. If the sequence $\{a_n\}$ is an arithmetic progression and the set $A = \{a_1, a_2, a_3, \ldots, a_m\}$ (where $m \in \mathbb{N}^*$, $m$ is a constant), then the expression for $L(A)$ in terms of $m$ is ______.

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