
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 and the positive $x$-axis as the polar axis, a polar coordinate system is established. The circle $\rho=4\cos \theta$ intersects with the circle $\rho=2\sin \theta$ at points $O$ and $A$.

(Ⅰ) Find the slope of line $OA$;  
(Ⅱ) A perpendicular line to $OA$ passing through point $O$ intersects the two circles at points $B$ and $C$, respectively. Find $|BC|$.

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