
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
Investigate the stability in the first approximation of the equilibrium point $x=0, y=0$ for the system

$$
\left\{\begin{array}{l}
\dot{x}=2 x+y-5 y^{2} \\
\dot{y}=3 x^{6}+y+\frac{x^{3}}{2}
\end{array}\left(\dot{x}=\frac{d x}{d t}, \quad \dot{y}=\frac{d y}{d t}\right)\right.
$$

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