
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 polar equation of curve \\(C\\) is \\(\rho=2\cos \theta\\), with the pole as the origin of the Cartesian coordinate system and the polar axis as the positive half-axis of \\(x\\), establish the Cartesian coordinate system. The parametric equation of line \\(L\\) is \\( \begin{cases} x= \dfrac { \sqrt {3}}{2}t+m \\\\ y= \dfrac {1}{2}t\end{cases} \\) (\\(t\\) is the parameter).
\\((1)\\) Find the Cartesian equation of curve \\(C\\) and the general equation of line \\(L\\);
\\((2)\\) Let point \\(P(m,0)\\), if line \\(L\\) intersects curve \\(C\\) at points \\(A\\) and \\(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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