
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 $\left\{a_{n}\right\}$, given $a_{0} = 1$, $a_{1} = 2$, and the recurrence relation $n(n+1) a_{n+1} = n(n-1) a_{n} - (n-2) a_{n-1}$ for $n \geq 1$, find $a_{n}$ for $n \geq 2$.

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