
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
Suppose that \((x_{0}, y_{0})\) is a solution of the system:
\[
\begin{cases}
xy = 6 \\
x^2 y + xy^2 + x + y + c = 2
\end{cases}
\]
Find the value of \(d = x_{0}^{2} + y_{0}^{2}\).

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