
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 $xoy$, the parametric equations of curve $C_{1}$ are $\left\{\begin{array}{l}{x=1+t}\\{y=\sqrt{3}t}\end{array}\right.$ (where $t$ is the parameter). Taking the coordinate origin as the pole and the positive $x$-axis as the polar axis, the polar coordinate equation of curve $C_{2}$ is ${ρ}^{2}=\frac{3}{2-cos2θ}$. <br/>$(1)$ Find the Cartesian equations of curves $C_{1}$ and $C_{2}$; <br/>$(2)$ If curves $C_{1}$ and $C_{2}$ intersect at points $A$ and $B$, and point $P(1,0)$, find the value of $\frac{1}{|PA|}+\frac{1}{|PB|}$.

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