
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
In the sequence ${a_{n}}$, $a_{1}=1$, and when $n\geqslant 2$, $a_{n}=a_{n-1}+n$. If the inequality $\frac{\lambda }{n} > \frac{n+1}{{{a}\_{n}}+1}$ holds for any $n\in\mathbb{N}^{*}$, then the range of the real number $\lambda$ is _______.

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