
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 $(xoy)$, a curve $C\_1$ is given by the parametric equations: $\begin{cases} x=\cos θ \ y=\sin θ\end{cases} (θ \text{ is a parameter})$. Establish a polar coordinate system with the origin $O$ as the pole, the non-negative semi-axis of the $x$-axis as the polar axis, and the same unit length as the rectangular coordinate system $(xoy)$. The polar equation of a line $l$ is given by $ρ(2\cos θ-\sin θ)=6$.

1. Write the parametric equations of the curve $C\_2$ obtained by stretching the horizontal and vertical coordinates of all points on the curve $C\_1$ by a factor of $\sqrt{3}$ and $2$, respectively. Also, write the rectangular equation of the line $l$.
2. Find a point $P$ on the curve $C\_2$ such that the distance from $P$ to line $l$ is maximized, and compute this maximum distance.

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