
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 $xoy$, the parametric equations of curve $C_1$ are given by $$\begin{cases} x=1- \frac { \sqrt {2}}{2}t \\ y=1+ \frac { \sqrt {2}}{2}t\end{cases}$$ (where $t$ is the parameter). In the 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 $C_2$ is $\rho\sin^2\theta=4\cos\theta$.

1. Find the Cartesian equation of curve $C_1$ and the polar equation of curve $C_2$.
2. If curves $C_1$ and $C_2$ intersect at points $A$ and $B$, and the polar coordinates of point $P$ are $(\sqrt{2}, \frac{\pi}{4})$, find the value of $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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