
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
In the rectangular coordinate system xOy, a polar coordinate system is established with the coordinate origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinate equation of the curve C is given by: $$ρ= \frac {4cosθ}{1-cos^{2}\theta }$$, and the parametric equation of the line l is $$\begin{cases} x=2+tcos\alpha \\ y=2+tsin\alpha \end{cases}$$ (t is the parameter, $0≤α<π$).

(1) Find the rectangular coordinate equation of curve C.

(2) Suppose line l intersects curve C at two points A and B, and the midpoint of segment AB is M (2, 2). Find the value of $α$.

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