
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 $U\_n = \{1,2,3,4,...,n\}$, where $n \in \mathbb{N}^*, n > 2$, and its subsets $A$ and $B$ satisfy: $A \cup B = U$, $A \cap B = \varnothing$, and the number of elements in set $A$ is not an element of set $A$, and the number of elements in set $B$ is not an element of set $B$. Let $a\_n$ denote the number of all different sets $A$ that meet the conditions. For example, for $U\_3 = \{1,2,3\}$, the sets $A$ that meet the conditions are $\{2\}$ and $\{1,3\}$, so $a\_3 = 2$.

1. $a\_6 =$ _______ ;
2. $a\_n =$ _______ $(n > 2)$.

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