
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 $(xOy)$, establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis. Given that the rectangular coordinates of point $P$ are $(-3,-\frac{3}{2})$, the polar equation of curve $C$ is $ρ=5$, and line $l$ passes through point $P$ intersecting curve $C$ at points $A$ and $B$.

1. Find the rectangular equation of curve $C$.
2. If $|AB|=8$, find the rectangular equation of line $l$.

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