
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:

\[
\begin{aligned}
& 3 x^{2}+2 y^{2}+2 x+3 y=0 \\
& 4 x^{2}-3 y^{2}-3 x+4 y=0
\end{aligned}
\]

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