
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, a circle C with center at point C(2, $\frac{\pi}{2}$) and radius 3 intersects with the line $l: \theta = \frac{\pi}{3}$ ($\rho = R$) at points A and B.  
(1) Find the standard equation of circle C and line l.  
(2) Find the length of chord |AB|.

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