
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 real number pairs \((x, y)\) that satisfy:
$$
\left\{
\begin{array}{l}
x^{2}+y^{2}+x+y=xy(x+y)-\frac{10}{27}, \\
|xy| \leq \frac{25}{9}.
\end{array}
\right.
$$

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