
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
If the sequence $\left\{ a_n \right\}$ satisfies $a_n-2a_{n+1}+a_{n+2}=0 \left( n\in \mathbb{N}^* \right)$, and $a_1=2, a_2=4$, then the general formula for the sequence $\left\{ a_n \right\}$ is $a_n=$               .

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