
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 the sequence $\left\{a_{n}\right\}$ where $a_{1} = a_{2} = 1$ and $a_{n} = \frac{a_{n-1}^{2} + 2}{a_{n-2}}$ for $n \geq 3$, find the general term $a_{n}$.

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