
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 curves \\(C_1:\\begin{cases}x=-4+\cos t \\ y=3+\sin t\end{cases} (t \\) is the parameter\\()), \\(C_2:\\begin{cases}x=8\cos \theta \\ y=3\sin \theta\end{cases} (\theta \\) is the parameter\\()). 

\\((1)\\) Convert the equations of \\(C_1,C_2 \\) into standard form;

\\((2)\\) If the point \\(P \\) on \\(C_1 \\) corresponds to the parameter \\(t= \dfrac{\pi}{2} \\), and \\(Q\\) is a moving point on \\(C_2 \\), find the minimum distance from the midpoint \\(M \\) of \\(PQ \\) to the line \\(C_3:\\begin{cases}X=3+2t \\ y=-2+t\end{cases} (t \\) is the parameter\\()).

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