
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 rectangular coordinate system $(xOy)$, a pole coordinate system is established with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. If the polar coordinate equation of the curve $C$ is $ρ\sin ^{2}θ+4\sin θ-ρ=0$, and the line $l$: $\begin{cases} x=2+ \frac { \sqrt {2}}{2}t \\ y=3+ \frac { \sqrt {2}}{2}t \end{cases}(t$ is the parameter$)$ intersects the curve $C$ at points $M$ and $N$.

1. Write the rectangular coordinate equation of the curve $C$ and the ordinary equation of the line $l$.
2. Find $|MN|$.

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