
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
In the sequence \(\{a_{n}\}\), it is known that \(a_{n+2}=3 a_{n+1}-2 a_{n}\), \(a_{1}=1\), and \(a_{2}=3\). Find the general term formula for the sequence \(\{a_{n}\}\).

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