
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 $\{1, 2, 3, \ldots, n\}$ (where $n \in \mathbb{N}^*$ and $n \geq 3$), if the set has subsets with the following properties: each subset contains at least two elements, and the absolute difference between any two elements in each subset is greater than 1, then these subsets are called T-subsets. Let $a_n$ be the number of T-subsets.
(1) If $a_n = 7$, then $n = \_\_\_\_\_\_$ ;
(2) $a_{10} = \_\_\_\_\_\_$.

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