
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 $n \geqslant 4$ be an integer. In the set $\{1, 2, 3, ..., n\}$, we pick two distinct elements $a$ and $b$ ($a > b$). Let $A_n$ denote the number of ways to pick $a$ and $b$ such that $a + b$ is divisible by $2$.

1. Find $A_n$ when $n = 6$.
2. Express $A_n$ in general.

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