
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
If a subset of the set $S$ satisfies: it contains at least $2$ elements, and the absolute difference between any two elements is greater than $1$, then this subset is called a super subset of the set $S$. Given the set ${A}_{n}=\{1,2,3,\ldots,n\}(n\in{N}^{*},n\geq3)$, let $a_{n}$ denote the number of super subsets of $A_{n}$. Find $a_{9}$.

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