
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
Find the sum of the roots of the equation \[(6+3\sqrt{3})x^2 + (3+\sqrt{3})x - 3 = 0.\]
A) $-\frac{2}{3} + \sqrt{3}$
B) $-1 + \frac{\sqrt{3}}{3}$
C) $\frac{1}{3} - \sqrt{3}$
D) $1 - \frac{\sqrt{3}}{3}$

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