
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 the parametric equation of curve $C\_1$ as $\begin{cases}x=-2-\frac{\sqrt{3}}{2}t, \\ y=\frac{1}{2}t\end{cases}$ ($t$ is the parameter), and the polar coordinate equation of curve $C\_2$ as $ρ=2\sqrt{2}\cos\left(\begin{matrix}θ-\frac{π}{4}\end{matrix}\right)$. Establish a plane rectangular coordinate system with the pole as the coordinate origin and the polar axis as the positive half of the $x$-axis.

(1) Find the rectangular coordinate equation of curve $C\_2$;

(2) Find the maximum distance from the moving point $M$ on curve $C\_2$ to curve $C\_1$.

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