
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
If \( (x, y) \) is a solution to the system
\[
\begin{align*}
xy &= 12, \\
x^2 y + xy^2 + x + y &= 110,
\end{align*}
\]
find \( x^2 + y^2 \).

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