
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
Find $x^2+y^2$ if $x$ and $y$ are positive integers such that 
\[
\begin{aligned} 
xy + x + y &= 35 \\
x^2y + xy^2 &= 306.
\end{aligned}
\]

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