
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
A sequence \(\left(a_{n}\right)\) satisfies the conditions:

$$
a_{1}=3, \quad a_{2}=9, \quad a_{n+1}=4 a_{n}-3 a_{n-1} \quad (n > 1)
$$

Find the formula for the general term of the sequence.

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