
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 plane rectangular coordinate system $(xOy)$, with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system. The parametric equations of the curve $C_{1}$ are given by $ \begin{cases} x= \sqrt {3}\cos θ \\ y=\sin θ \end{cases}(θ \text{ is the parameter })$, and the polar coordinate equation of the curve $C_{2}$ is $ρ\cos θ-ρ\sin θ-4=0$.

1. Find the Cartesian equation of curve $C_{1}$ and the rectangular coordinate equation of curve $C_{2}$;
2. Let $P$ be a point on curve $C_{1}$, find the maximum value of the distance $|PQ|$ from point $P$ to curve $C_{2}$.

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