
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 \(\left\{a_{n}\right\}, n \in \mathbf{N}_{+}\), where \(a_{1}=1\) and \(a_{n}=a_{1} a_{2} \cdots a_{n-1}+1\) for \(n \geq 2\). Find the smallest real number \(M\) such that for any \(m \in \mathbf{N}_{+}\), \(\sum_{n=1}^{m} \frac{1}{a_{n}} < M\).

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