
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 exist real numbers $x$ and $y$ such that
\[\begin{pmatrix} 3 \\ -1 \end{pmatrix} + x \begin{pmatrix} 8 \\ -3 \end{pmatrix} = \begin{pmatrix} 0 \\ 2 \end{pmatrix} + y \begin{pmatrix} -1 \\ 4 \end{pmatrix}.\]
Enter the ordered pair $(x, y)$.

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