
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 a line \\(l\\) passing through the point \\(P(m,0)\\) with the parametric equation \\(\begin{cases} & x=\dfrac{\sqrt{3}}{2}t+m \\\\ & y=\dfrac{1}{2}t \end{cases}\\) (where \\(t\\) is the parameter). Using the origin of the 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 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}
user