
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 $\left\{a_{n}\right\}$ that satisfies the conditions: $a_{1}=1$, $a_{2}=2$, and for any three consecutive terms $a_{n-1}, a_{n}, a_{n+1}$, the relation $a_{n}=\frac{(n-1) a_{n-1}+(n+1) a_{n+1}}{2 n}$ holds. Determine the general term $a_{n}$.

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