
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 \( x_{1}=1 \), \( x_{2}=6 \), and \( x_{n+1}=6 x_{n}-9 x_{n-1}+3^{n} \) for \( n=2,3, \cdots \), find the general term formula for the sequence \(\{ x_{n} \}\).

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