
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 all pairs  $(x,y)$  of real numbers that satisfy,
\begin{align*}
    x^2+y^2+x+y &= xy(x+y)-\frac{10}{27}
    |xy| & \leq \frac{25}{9}.
\end{align*}


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