
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 polar coordinate system, it is known that circle C passes through point P ($$\sqrt {2}$$, $$\frac {π}{4}$$), and the center of the circle is the intersection point of the line $$ρ\sin（θ- \frac {π}{3}$$）= -$$\frac { \sqrt {3}}{2}$$ with the polar axis.  
(1) Find the polar equation of circle C;  
(2) Find the length of the chord cut by the line $$θ= \frac {π}{3}$$ ($$ρ∈R$$) on circle C.

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