
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 all values of the angle \(\alpha\) in the interval \(\left[0^{\circ} ; 360^{\circ}\right]\) such that the system of equations

$$
\left\{
\begin{array}{l}
y^{3} \geqslant 3 x^{2} y \\
(x-\cos \alpha)^{2}+(y-\sin \alpha)^{2}=\frac{2-\sqrt{3}}{4}
\end{array}
\right.
$$

has a unique solution.

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