
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 following conclusions:

A moving point \\(M(x,y)\\) has the product of the slopes of its lines to two fixed points \\((-3,0)\\) and \\((3,0)\\) equal to \\( \dfrac{16}{9} \\). Let the trajectory of \\(M(x,y)\\) be curve \\(C\\), and let \\(F_{1}\\) and \\(F_{2}\\) respectively be the left and right foci of curve \\(C\\). Among the following propositions:

\\((1)\\) The coordinates of the foci of curve \\(C\\) are \\(F_{1}(-5,0)\\) and \\(F_{2}(5,0)\\);

\\((2)\\) If \\(\angle F_{1}MF_{2}=90^{\circ}\\), then \\(S\Delta{F}_{1}MF_{2} =32\\);

\\((3)\\) When \\(x < 0\\), the center of the inscribed circle of \\(\triangle F_{1}MF_{2}\\) lies on the line \\(x=-3\\);

\\((4)\\) Let \\(A(6,1)\\), then the minimum value of \\(|MA|+|MF_{2}|\\) is \\(2 \sqrt{2} \\); the correct proposition numbers are: \_\_     ．

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