
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 $\{a_n\}$ that satisfies $na_{n+2}-(n+2)a_{n}=\lambda(n^{2}+2n)$, where $a_{1}=1$, $a_{2}=2$, if $a_{n} < a_{n+1}$ holds for $\forall n\in\mathbb{N}^{*}$, then the range of the real number $\lambda$ is \_\_\_\_\_\_.

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