
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 $\{a\_n\}$ where all terms are positive, the first term $a\_1=2$, and the point $(a\_n^2,a_{n-1}^2)$ is on the line $x-9y=0$, then the sum of the first $n$ terms of the sequence, $S\_n$, is equal to $\_\_\_\_\_\_\_\_\cdot$

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