
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 O as the pole and the positive x-axis as the polar axis, a polar coordinate system is established. It is known that the circle C has its center at the polar coordinates: C($$\sqrt{2}$$, $$\frac{\pi}{4}$$), and radius r = $$\sqrt{3}$$.
(1) Find the polar equation of circle C;
(2) If a line l passing through point P(0, 1) with a slope angle $$\alpha = \frac{\pi}{6}$$ intersects circle C at points A and B, find the value of |PA|^2 + |PB|^2.

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