
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 system of equations:
\[
\left\{
\begin{array}{l}
x^{2} y - x y^{2} - 3 x + 3 y + 1 = 0, \\
x^{3} y - x y^{3} - 3 x^{2} + 3 y^{2} + 3 = 0.
\end{array}
\right.
\]

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