
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 graph of the quadratic polynomial

$$
y=\frac{2}{\sqrt{3}} x^{2}+b x+c
$$

intersects the positive half-axis of the $Oy$ axis at the point $M$, and the positive half-axis of the $Ox$ axis at the points $K$ and $L$ (point $L$ is located to the right of point $K$). It turned out that $\angle L K M=120^{\circ}$, and $K L=K M$. Find the roots of this polynomial.

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