
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 $\left\{a_{n}\right\}$ which satisfies $a_{1}=a_{2}=1, a_{3}=2, \text{ and } 3a_{n+3}=4a_{n+2}+a_{n+1}-2a_{n}, \text{ for } n=1,2, \cdots,$ find the general term of the sequence $\left\{a_{n}\right\}$.

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