
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
Consider the function defined by:
\[ y = \sqrt{9x^2 - 6x + 1} - \sqrt{9x^2 + 6x + 1} + 2x^2 \]
A) \( |3x-1| - |3x+1| - 2x^2 \)
B) \( 3x-1 - 3x-1 + 2x^2 \)
C) \( |3x-1| - |3x+1| + 2x^2 \)
D) \( |3x+1| - |3x-1| + 2x^2 \)

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