
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 $(x)O(y)$, a point $P(1,-2)$ and a line $l$: $\begin{cases}x=1+t \\ y=-2+t\end{cases} (t$ is a parameter$)$ are given. 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 the curve $C$ is $\rho \sin^2 \theta = 2 \cos \theta$, and the intersection points of the line $l$ and the curve $C$ are $A$ and $B$.

(1) Find the general equation of the line $l$ and the Cartesian equation of the curve $C$.

(2) Calculate $|PA|+|PB|$.

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