
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 a sequence \(\{a_n\}\) such that: \(a_1 = 1\) and \(a_{n+1} = \frac{a_n}{(n+1)(a_n + 1)}\) for \(n \in \mathbb{Z^+}\), find the value of \(\lim_{n \rightarrow +\infty} n! \cdot a_n\).

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