
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 positive sequence $a_0$, $a_1$, $a_2$, ..., $a_n$, ... satisfy  
    $a_n = 2a_{n-1} - a_{n-2}$, (for $n \geq 2$)  
and $a_0 = a_1 = 1$, find the general formula for the sequence $\{a_n\}$.

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