
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
Given matrices $$A= \begin{bmatrix} -1 & 2 \\ 1 & x\end{bmatrix}$$ and $$B= \begin{bmatrix} 1 & 1 \\ 2 & -1\end{bmatrix}$$, and vector $$\overrightarrow {a} = \begin{bmatrix} 2 \\ y\end{bmatrix}$$, if $$A\overrightarrow {a} = B\overrightarrow {a}$$, find the values of the real numbers $x$ and $y$.

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