
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 $a_1=1$, $a_2=2$, and $2na_n=(n-1)a_{n-1}+(n+1)a_{n+1}$ for $n \geq 2$ and $n \in \mathbb{N}^*$, find $a_{18}$.

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