
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 O and the positive x-axis as the polar axis, the polar equation of circle C is $\rho=4\sqrt{2}\cos(\theta+ \frac{\pi}{4})$.
(1) Convert the polar equation of circle C into a Cartesian coordinate equation;
(2) A line l with a slope of 1 passes through point P(2,0) and intersects circle C at points A and B. Calculate the value of $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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