
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 rectangular coordinate system <sub>\(xOy \)</sub>, a polar coordinate system is established with the origin _\\(O\\)_ as the pole and the positive semi-axis of the _\\(x\\)_-axis as the polar axis. The curves \\(C\_{1}\\) and \\(C\_{2}\\) are given by the parametric equations:

\\(C\_{1}\\): <sub>\(\begin{cases}x=-4+\cos t, \\ y=3+\sin t,\end{cases} \)</sub> \\((t\\) is the parameter\\()\\)

\\(C\_{2}\\): <sub>\(\begin{cases}x=8\cos θ \\ y=3\sin θ\end{cases} \)</sub>\\((θ \\) is the parameter\\()\\)

(I) Convert the equations of \\(C\_{1}\\) and \\(C\_{2}\\) into standard forms and describe the curves they represent.

(II) If the parameter corresponding to point \\(P\\) on curve \\(C\_{1}\\) is <sub>\(t= \dfrac{π}{2} \)</sub>, and \\(Q\\) is a moving point on curve \\(C\_{2}\\), find the minimum distance from the midpoint \\(M\\) of \\(PQ\\) to the line <sub>\({C}_{3}:p\left(\cos θ-2\sin θ\right)=7 \)</sub>.

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