
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 $(xOy)$, given point $P(1,-2)$, line $l$: $\begin{cases}x=1+ \frac{ \sqrt{2}}{2}t \\ y=-2+ \frac{ \sqrt{2}}{2}t\end{cases} (t$ is a parameter$)$, establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is $\rho\sin ^{2}\theta=2\cos \theta$. The intersection points of line $l$ and curve $C$ are $A$ and $B$.

1. Find the ordinary equations of line $l$ and curve $C$.
2. Calculate the value of $|PA|+|PB|$.

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