
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
Consider the sequence \(\{a_n\}\) with the sum of its first \(n\) terms denoted as \(S_n\). The sequence satisfies \(S_n + S_{n+1} + S_{n+2} = 6n^2 + 9n + 7\) for \(n \geq 1\). Given that \(a_1 = 1\) and \(a_2 = 5\), find the general term formula for the sequence \(\{a_n\}\).

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