
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 $A= \begin{bmatrix} 2 & -1 \\ -4 & 3 \end{bmatrix}$, $B= \begin{bmatrix} 2 & -2 \\ -4 & 6 \end{bmatrix}$.  
(1) Find the inverse matrix of $A$;  
(2) Find the second-order matrix $X$ that satisfies $AX=B$.

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