
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
In the Cartesian coordinate system \\(xOy\\), the parametric equation of curve \\(C_{1}\\) is given by \\(\begin{cases}x= \frac{1}{2}t \\ y=m+ \frac{ \sqrt{3}}{2}t\end{cases} (t\\) is the parameter). In the polar coordinate system with the origin \\(O\\) as the pole and the positive x-axis as the polar axis, the polar equation of curve \\(C_{2}\\) is \\(\rho=4\cos \left(\theta- \frac{\pi}{6}\right) \\).
\\((1)\\) Write the Cartesian equation of the curve \\(C_{2}\\).
\\((2)\\) Suppose points \\(P\\) and \\(Q\\) are on curves \\(C_{1}\\) and \\(C_{2}\\) respectively, and the minimum value of \\(|PQ|\\) is \\(1\\). Find the value of \\(m\\).

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