
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 $M= \begin{pmatrix} 2 & a \\ 2 & b \end{pmatrix}$ with two eigenvalues $\lambda_1 = -1$ and $\lambda_2 = 4$,
(Ⅰ) Find the values of the real numbers $a$ and $b$;
(Ⅱ) If the image of the line $l$ under the linear transformation corresponding to matrix $M$ is given by the equation $x-2y-3=0$, find the equation of the line $l$.

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