
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 \(\{a_n\}\), \(a_1 = 1\), \(a_2 = 2\), \(a_{n+2} = 5a_{n+1} - 6a_n\) for \(n = 1, 2, 3, \cdots\), find the general term formula for \(\{a_n\}\).

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