
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 Cartesian coordinate system $xOy$, with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of circle $C$ is $$\rho=4 \sqrt {2}\sin\left( \frac {3\pi}{4}-\theta\right)$$  
(1) Convert the polar equation of circle $C$ into a Cartesian coordinate equation;  
(2) Draw a line $l$ with slope $\sqrt {3}$ through point $P(0,2)$, intersecting circle $C$ at points $A$ and $B$. Calculate the value of $$\left| \frac {1}{|PA|}- \frac {1}{|PB|}\right|.$$

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