
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 \(\left\{a_{n}\right\}\) satisfying:
\[
\begin{array}{l}
a_{1}=1, \quad a_{2}=\frac{1}{3}, \\
a_{n} a_{n-1}+a_{n} a_{n+1}=2 a_{n-1} a_{n+1} \quad (n \geq 2, \, n \in \mathbb{Z}_{+}) .
\end{array}
\]
find the general term of the sequence.

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