
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
This question includes two sub-questions, B and C, from the elective subjects 4-2: Matrix and Transformation, and 4-4: Polar Coordinates and Parametric Equations, in the college entrance examination. Each sub-question is worth 10 points, making a total of 20 points. Write your answers in the corresponding sections of the answer sheet. When solving, you should provide explanations, proof processes, or calculation steps.

B. Elective 4-2: Matrix and Transformation  
Given the matrix $$A= \begin{bmatrix} 1 & 1 \\ 2 & 1\end{bmatrix}$$, and the vector $$\overrightarrow {\beta }= \begin{bmatrix} 1 \\ 2\end{bmatrix}$$．Find the vector $$\overrightarrow {\alpha }$$ such that $$A^{2} \overrightarrow {\alpha }= \overrightarrow {\beta }$$．  

C. Elective 4-4: Polar Coordinates and Parametric Equations  
In the Cartesian coordinate system x0y, the parametric equation of line l is $$\begin{cases} x= \frac {1}{2}t \\ y= \frac { \sqrt {2}}{2}+ \frac { \sqrt {3}}{2}t\end{cases}$$ (t is the parameter). If the origin O of the Cartesian coordinate system xOy is taken as the pole and Ox as the polar axis, with the same unit length, establishing a polar coordinate system, the polar equation of curve C is $$\rho =2cos(\theta - \frac {\pi }{4})$$．  
(1) Find the slope angle of line l;  
(2) If line l intersects curve C at points A and B, find the length of AB．

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