
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 systems of equations:
a) 
\[
\begin{cases}
x + y + xy = 5, \\
xy(x + y) = 6;
\end{cases}
\]

b) 
\[
\begin{cases}
x^3 + y^3 + 2xy = 4, \\
x^2 - xy + y^2 = 1.
\end{cases}
\]

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