
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
The system

$$
\begin{aligned}
& (x - y)\left( x^2 - y^2 \right) = 160 \\
& (x + y)\left( x^2 + y^2 \right) = 580
\end{aligned}
$$

has a pair of solutions $x_{1} = 3, y_{1} = 7$. What other pair of solutions should this system have?

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