
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
Specify all values of \(a\), for which the system of equations 
\[
\left\{
\begin{array}{c}
x - 4 = a\left(y^{3} - 2\right), \\
\frac{2x}{\left|y^{3}\right| + y^{3}} = \sqrt{x}
\end{array}
\right.
\]
has at least one solution, and solve it for each \(a\).

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