
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
Use the knowledge of inverse matrices and determinants to solve for $X=\begin{pmatrix} x \\ y \end{pmatrix}$ in the equation $MX=N$, where $M=\begin{pmatrix} 5 & 2 \\ 4 & 1 \end{pmatrix}$, and $N=\begin{pmatrix} 5 \\ 8 \end{pmatrix}$.  
(No points will be awarded if the problem is not solved as required)  
Method 1: (Inverse Matrix Method)  
Method 2: (Determinant Method)

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