
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
The equation \(\frac{3x^2}{x-2}-\frac{3x+10}{4}+\frac{5-9x}{x-2}+2=0\) can be simplified by eliminating the fractions, resulting in a transformed equation. Determine the roots of the transformed equation and then identify the roots of the original equation.
**A)** \(2.76\) only  
**B)** \(-0.18\) only  
**C)** Both \(2.76\) and \(-0.18\)  
**D)** Neither \(2.76\) nor \(-0.18\)  
**E)** Other roots

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