
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 parametric equations of curve C as $$\begin{cases} x=3\cos\theta \\ y=2\sin\theta \end{cases}$$ (where $\theta$ is the parameter), in the same Cartesian coordinate system, the points on curve C are transformed according to $$\begin{cases} x'= \frac {1}{3}x \\ y'= \frac {1}{2}y \end{cases}$$ to obtain curve C'. Taking the origin as the pole and the positive x-axis as the polar axis, a polar coordinate system is established.  
(1) Write the polar equations of curves C and C';  
(2) If a line $l$ passing through point $A(2 \sqrt {2}, \frac {\pi}{4})$ (in polar coordinates) with a slope angle of $\frac {\pi}{3}$ intersects curve C at points M and N, and the midpoint of chord MN is P, find the value of $\frac {|AP|}{|AM|\cdot |AN|}$.

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