
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

There is a pair of roots for the system

$$
\begin{gathered}
2 x^{2} + 3 x y + y^{2} = 70 \\
6 x^{2} + x y - y^{2} = 50
\end{gathered}
$$

given by \( x_{1} = 3 \) and \( y_{1} = 4 \); find another pair of roots.

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