
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 a Cartesian coordinate system, the parametric equation of curve \\(C_{1}\\) is given by
$$
\begin{cases}
x=3\cos \alpha \\
y=\sqrt{3}\sin \alpha
\end{cases}
(\alpha \text{ is the parameter}),
$$
and a polar coordinate system is established with the origin as the pole, the positive half-axis of \\(x\\) as the polar axis, and the same unit length as in the Cartesian coordinate system. The polar equation of curve \\(C_{2}\\) is
$$
\rho=2\cos \theta.
$$
\\((1)\\) Find the Cartesian coordinate equations of \\(C_{1}\\) and \\(C_{2}\\).
\\((2)\\) Let \\(P\\) and \\(Q\\) be any points on \\(C_{1}\\) and \\(C_{2}\\), respectively; find the minimum value of \\(|PQ|\\).

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