
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
Elective 4-4: Coordinate System and Parametric Equations

Given a line $l$ passing through point $P(m,0)$, the parametric equation of line $l$ is $\begin{cases}x= \dfrac{ \sqrt{3}}{2}t \\ y= \dfrac{1}{2}t\end{cases} (t$ is the parameter$).$ With the origin of the plane Cartesian coordinate system as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is $\rho=2\cos \theta .$

(Ⅰ) Find the general equation of line $l$ and the Cartesian coordinate equation of curve $C$;

(Ⅱ) If line $l$ intersects curve $C$ at two points $A$, $B$, and $|PA|\cdot|PB|=1$, find the value of the real number $m$.

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