
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
A coordinate system and parametric equations (4-4)

Given that the polar coordinate equation of circle $E$ is $ρ=4\sin θ$, establish a planar rectangular coordinate system with the pole as the origin and the positive half of the polar axis as the $x$-axis, using the same unit length (where $(ρ,θ)$, $ρ≥0$, $θ∈[0,2π]$).
1. Line $l$ passes through the origin with an inclination angle of $α=\frac{3π}{4}$. Find the polar coordinates of the intersection point $A$ of line $l$ and circle $E$ (point $A$ is not the coordinate origin);
2. Line $m$ passes through the midpoint $M$ of segment $OA$ and intersects circle $E$ at points $B$ and $C$. Find the maximum value of $||MB|-|MC||$.

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