
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 set $A=\{1,2,\ldots,n\}$, where $n\geq4$, $n\in\mathbb{N}^{*}$. If $X\subseteq A$, and $2\leq\text{Card}(X)\leq n-2$ (where $\text{Card}(X)$ represents the number of elements in set $X$), let $a_X$ represent the sum of the largest and smallest numbers in $X$, then  
(1) When $n=5$, the number of sets $X$ is $\boxed{20}$.  
(2) The average value of all $a_X$ is $\boxed{n+1}$.

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