
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 defined by \( a_{0}=3, a_{1}=9, a_{n}=4a_{n-1}-3a_{n-2}-4n+2 \) for \( n \geq 2 \), find the general term formula for the sequence \(\{a_n\}_{n \geqslant 0}\).

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