
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 $\rho=4\sin \theta$, with the pole as the origin and the polar axis as the positive half of the $x$-axis, establish a Cartesian coordinate system with the same unit length (where $(\rho,\theta)$, $\rho \geqslant 0$, $\theta \in [0,2\pi)$).  
$(1)$ Line $l$ passes through the origin, and its inclination angle $\alpha= \dfrac {3\pi}{4}$. Find the polar coordinates of the intersection point $A$ of $l$ and circle $E$ (point $A$ is not the origin);  
$(2)$ 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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