
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
(Ⅰ) Given the matrices $A= \begin{pmatrix} 0 & 1 \\ a & 0\end{pmatrix}$ and $B= \begin{pmatrix} 0 & 2 \\ b & 0\end{pmatrix}$, the line $l_1$ with equation $x-y+4=0$ is transformed by the matrix $A$ to become line $l_2$, and line $l_2$ is further transformed by matrix $B$ to become line $l_3$ with equation $x+y+4=0$. Find the equation of line $l_2$.  
(Ⅱ) Find the length of the chord cut by the line $\begin{cases} x=-1+2t \\ y=-2t\end{cases}$ on the curve $\begin{cases} x=1+4\cos\theta \\ y=-1+4\sin\theta \end{cases}$.

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