
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 $\left\{a_{n}\right\}$, let $a_{1}=1$ and $a_{n} \neq 0$ for $n \in \mathbf{N}_{+}$. If $a_{n}+2 a_{n} a_{n-1}-a_{n-1}=0$ for $n \geqslant 2$ and $n \in \mathbf{N}_{+}$, then $a_{n}=$ $\qquad$

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