
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
Taking the origin $O$ of the Cartesian coordinate system as the pole and the positive half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is given by $\rho\sin^2\theta=4\cos\theta$.  
(1) Find the Cartesian equation of curve $C$.  
(2) If the parametric equation of line $l$ is $\begin{cases} x=1+ \frac {2}{ \sqrt {5}}t \\ y=1+ \frac {1}{ \sqrt {5}}t \end{cases}$ (where $t$ is the parameter), and let point $P$ be $(1,1)$, line $l$ intersects curve $C$ at points $A$ and $B$. Find the value of $|PA|+|PB|$.

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