
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
Optional Question  
A. Elective 4-2 Matrix and Transformation  
Given the matrix $$A= \begin{vmatrix} 1 & 2 \\ -1 & 4\end{vmatrix}$$, and the vector $$\overrightarrow {a} = \begin{vmatrix} 7 \\ 4\end{vmatrix}$$．  
(Ⅰ) Find the eigenvalues λ<sub>1</sub>, λ<sub>2</sub> and eigenvectors α<sub>1</sub>, α<sub>2</sub> of A; (Ⅱ) Calculate the value of A<sup>6</sup>α.  
B. Elective 4-4 Coordinate System and Parametric Equation  
Given the parametric equation of line l is $$\begin{cases} x=4-2t \\ y=t-2\end{cases}$$ (t is the parameter), P is any point on the ellipse $$\frac {x^{2}}{4}+y^{2}=1$$, find the maximum distance from point P to line l.

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