
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 $A=\{1,2,...,n\}$, where $n\geqslant 4$, $n\in\mathbb{N}^*$, and $X\subseteq A$ with $2\leqslant \text{Card}(X)\leqslant n-2$. Let $a\_X$ denote the sum of the maximum and minimum numbers in $X$. Find:

1. The number of sets $X$ when $n=5$.
2. The average value of all $a\_X$.

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