
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 $\{a_n\}$, we have $a_1=1$, and for $n \geqslant 2$, $a_n=a_{n-1}+n$. If the inequality $\frac{λ}{n} > \frac{n+1}{a_n+1}$ is satisfied for any $n \in \mathbb{N}^{*}$, then the range of the real number $λ$ is __________.

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