
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

Solve the following system of equations. It has a solution if and only if each term equals zero:

$$
\left\{\begin{array}{c}
3 x^{2}+8 x-3=0 \\
3 x^{4}+2 x^{3}-10 x^{2}+30 x-9=0
\end{array}\right.
$$

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