
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 $n$ be an integer where $n \geq 4$. In the set $\{1, 2, 3, \ldots, n\}$, select any two different elements $a$ and $b$ ($a > b$). Let $A_n$ be the number of ways to select $a$ and $b$ such that $a+b$ is divisible by 2.
(1) When $n=6$, find $A_n$;
(2) Find $A_n$ for any $n$.

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