
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
Let the sequence $\{a_n\}$ satisfy: $a_1 = 3$, and $n(a_{n+1} - a_n) = a_n + 1$ $(n \in \mathbb{N})$. If for any $a \in [-1,1]$ and $n \in \mathbb{N}$, the inequality $\frac{a_{n+1}}{n+1} < t^2 - 2at + 1$ always holds, then the range of values for the real number $t$ is ______.

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