
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 with pole O, the curve C1: ρ=2 and the curve C2: $$ρ\sin(θ-\frac{π}{4})=\sqrt{2}$$ intersect at two distinct points A and B.
(1) Find the value of |AB|;
(2) Find the polar coordinate equation of the line l that passes through point C(1,0) and is parallel to line AB.

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