
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 $xOy$, point $P(1,-2)$ is given, and line $l$ is defined by the parametric equations $\begin{cases} x=1+t \\ y=-2+t\end{cases}$ (where $t$ is the parameter). With the origin as the pole and the positive $x$-axis as the initial line, a polar coordinate system is established. 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 standard equations of line $l$ and curve $C$;
$(2)$ Find $|PA|+|PB|$.

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