
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 \(\left\{a_{n}\right\}\) satisfies:
$$
\frac{a_{n+1}+a_{n}-1}{a_{n+1}-a_{n}+1}=n \quad (n \in \mathbf{Z}_{+}),
$$
and \(a_{2}=6\).

Find the general term formula for the sequence \(\left\{a_{n}\right\}\).

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