
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 \\(\{a_n\}\\) with the sum of the first \\(n\\) terms being \\(S_n\\), and \\(a_2=4\\), \\(S_4=30\\). For \\(n \geqslant 2\\), \\(a_{n+1}+a_{n-1}=2(a_n+1)\\), find the general formula for \\(a_n=\\) ______.

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