
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 the matrix $$A= \begin{bmatrix} 2 & 1 \\ 3 & 2\end{bmatrix}$$, and the column vector $$X= \begin{bmatrix} x \\ y\end{bmatrix}, B= \begin{bmatrix} 4 \\ 7\end{bmatrix}$$, if AX=B, directly write out $A^{-1}$, and find X.

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