
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, the parametric equations of curve $C_{1}$ are $\left\{\begin{array}{l}x=2+\cos\alpha-\sin\alpha\\ y=\sin\alpha+\cos\alpha\end{array}\right.$ ($\alpha$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis. The polar coordinate equation of curve $C_{2}$ is $ρ\sin(θ+\frac{π}{4})-\frac{\sqrt{2}}{2}=0$. <br/>$(1)$ Find the general equation of curve $C_{1}$ and the rectangular coordinate equation of curve $C_{2}$; <br/>$(2)$ Given the point $P(1,0)$, curves $C_{1}$ and $C_{2}$ intersect at points $A$ and $B$, find the value of $\frac{1}{|PA|}+\frac{1}{|PB|}$.

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