
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 
\[
\begin{cases} 
    x^{2}y - xy^{2} - 5x + 5y + 3 = 0, \\
    x^{3}y - xy^{3} - 5x^{2} + 5y^{2} + 15 = 0.
\end{cases}
\]

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