
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
The sequence  ${a_{n}}$   $n\in \mathbb{N}$  is given in a recursive way with  $a_{1}=1$ , $a_{n}=\prod_{i=1}^{n-1} a_{i}+1$ , for all  $n\geq 2$ .
Determine the least number  $M$ , such that  $\sum_{n=1}^{m} \frac{1}{a_{n}} <M$  for all  $m\in \mathbb{N}$ 

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