
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 M= $$\begin{bmatrix} a & b \\ -1 & 2\end{bmatrix}$$ with two eigenvalues λ<sub>1</sub>\=2, λ<sub>2</sub>\=3. Find the equation of the line l': x-y+2=0 under the transformation of matrix M.

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