
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 $\{a_n\}$ where $a_1=2$ and $n(a_{n+1}-a_{n}) = a_{n} + 1$ for $n \in \mathbb{N}^*$. For any $t \in [0, 1]$ and $n \in \mathbb{N}^*$, the inequality $\frac{a_{n+1}}{n+1} < -2t^2 - (a+1)t + a^2 - a + 3$ always holds. Determine the range of the real number $a$.

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