
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 a matrix $M$ with an eigenvalue $\lambda_{1}=8$ and its corresponding eigenvector $a_{1}=[1, 1]$, and the transformation corresponding to the matrix $M$ transforms the point $(-1,2)$ into $(-2,4)$
(I) Find the matrix $M$;
(II) If line $l$ is transformed into line $l′$: $x-2y=4$ under the linear transformation corresponding to matrix $M$, find the equation of line $l$.

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