
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 a fixed circle \\(M\\): \\((x-3)^{2}+y^{2}=16\\) and a fixed point \\(A\\) in the plane of circle \\(M\\). Let \\(P\\) be a moving point on circle \\(M\\), and the perpendicular bisector of segment \\(PA\\) intersects line \\(PM\\) at point \\(Q\\).  
\\((\\)I\\()\\) Discuss which of the following situations the trajectory of point \\(Q\\) could be: \\(①\\) Ellipse; \\(②\\) Hyperbola; \\(③\\) Parabola; \\(④\\) Circle; \\(⑤\\) Straight line; \\(⑥\\) A single point.  
\\((\\)II\\()\\) If the fixed point \\(A\\) is \\(A(5,0)\\), try to find the maximum area of \\(\\triangle QMA\\).

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