
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 equation $\frac{3x^2}{x-2}-\frac{3x+4}{2}+\frac{5-9x}{x-2}+2=0$. Transform this equation by eliminating fractions and solve for the roots.
A) $2 + \sqrt{6}$ and $2 - \sqrt{6}$
B) $2 + \sqrt{5}$ and $2 - \sqrt{5}$
C) $2 + \sqrt{7}$ and $2 - \sqrt{7}$
D) Only $2 + \sqrt{6}$
E) Only $2 - \sqrt{6}$

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