
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
Given a Cartesian coordinate system $(xOy)$ with its origin as the pole and the non-negative semi-axis of $x$ as the polar axis, a polar coordinate system is established with the same unit length for both systems. The polar coordinates of point $N$ are $(\sqrt{2}, \frac{\pi}{4})$, and $M$ is any point on the curve ${C_1}: \rho = 1$. Point $G$ satisfies $\overrightarrow{OG} = \overrightarrow{OM} + \overrightarrow{ON}$, and its trajectory forms a curve ${C_2}$.

(1) Find the Cartesian coordinate equation for the curve ${C_2}$;
(2) If the parametric equations of line $l$ passing through point $P(2, 0)$ are $\begin{cases} x = 2 - \frac{1}{2}t \\ y = \frac{\sqrt{3}}{2}t \end{cases} (t \text{ as a parameter})$, and the line $l$ intersects the curve ${C_2}$ 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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