
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
Sectional Exercise $(4-4)$: Coordinate Systems and Parametric Equations
Given that the polar coordinate equation of curve $C_{1}$ is $ρ = 4 \cos θ$, establish a rectangular coordinate system with the pole as the origin and the polar axis as the positive direction of the $x$-axis. The parametric equations of the line are: $ \begin{cases} x=2+t\cos θ \\ y=1+t\sin θ \end{cases}($ where $t$ is the parameter$)$.
(I) Find the rectangular coordinate equation of curve $C_{1}$;
(II) Suppose the line intersects curve $C_{1}$ at points $A$ and $B$, and point $M$ has rectangular coordinates $(2,1)$. If $\overrightarrow{AB}=3\overrightarrow{MB}$, find the general equation of the line.

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