
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
Given the polar equation of circle E is $\rho=4\sin\theta$, establish a Cartesian coordinate system with the pole as the origin and the positive half-axis of the polar axis as the x-axis, using the same unit length (where $\rho\geq0$, $\theta\in[0,2\pi)$). If the slope angle is $\frac{3\pi}{4}$ and the line $l$ passing through the origin intersects circle E at point A (point A is not the origin).  
(1) Find the polar coordinates of point A;  
(2) Suppose line $m$ passes through the midpoint M of segment OA, and line $m$ intersects circle E at points B and C, find the maximum value of $||MB|-|MC||$.

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