
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 that $n \in \mathbb{N}_+$ and $n \geq 4$, the sequence $T: a_1, a_2, \ldots, a_n$ consists of distinct terms, each belonging to the set $M = \{1, 2, \ldots, n\}$.
1. If $n=7$ and $a_2 < a_3 < a_4 < a_5 < a_6$, find the number of such sequences $T$.
2. If there is a unique term $a_k (k \in \mathbb{N}_+, k < n)$ in sequence $T$ such that $a_k > a_{k+1}$, find the number of all possible sequences $T$ that satisfy this condition.

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