
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
Consider the origin \\(O\\) as the pole and the positive half of the \\(x\\)-axis as the polar axis in a polar coordinate system. Let the curve \\({C_1}\\) be given by the parametric equations \\(\begin{cases} x = -2 + 2\cos t \\ y = 1 + 2\sin t \end{cases}\\) (with \\(t\\) as the parameter), and the curve \\({C_2}\\) by the polar equation \\(4\rho\cos\theta - \rho\sin\theta +1 = 0\\).

   \\((1)\\) Find the ordinary (Cartesian) equation of \\({C_1}\\) and the Cartesian equation of \\({C_2}\\).

   \\((2)\\) Let point \\(P\\) be on curve \\({C_1}\\) and point \\(Q\\) be on curve \\({C_2}\\). Determine the minimum value of \\(|PQ|\\).

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