
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 $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is $\rho\sin^2\theta=4\cos\theta$, and the parametric equation of line $l$ is $\begin{cases} x=2+\frac{\sqrt{2}}{2}t \\ y=\frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter).

(Ⅰ) Write the Cartesian equation of curve $C$ and the Cartesian equation of line $l$.

(Ⅱ) Given the point $P(2,0)$, line $l$ intersects curve $C$ at points $A$ and $B$. Find the length of the segment $|PA|+|PB|$.

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