
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
Let the sequence $\{a_n\}$ be defined by $a_1 = 3$, $a_2 = 8$, and $a_{n+2} = 2a_{n+1} + 2a_n$ for $n = 1, 2, \cdots$. Find the general term $a_n$ of the sequence $\{a_n\}$.

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