
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
Determine the real solutions to $\frac{3x^2}{x-2} - \frac{3x+9}{4} + \frac{6-9x}{x-2} + 2 = 0$, keeping in mind that solutions must also satisfy $x^3 \neq 3x + 1$.
A) $\frac{13}{9}$
B) $\frac{9}{13}$
C) $\frac{10}{3}$
D) No real solutions

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