
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]


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Given a circle \\(M\\) with a radius of \\(3\\), and its center is on the positive half of the \\(x\\)-axis. The line \\(3x-4y+9=0\\) is tangent to circle \\(M\\).

\\((1)\\) Find the standard equation of circle \\(M\\);

\\((2)\\) A line \\(l\\) passing through point \\(N(0,-3)\\) intersects circle \\(M\\) at two distinct points \\(A(x_{1},y_{1})\\) and \\(B(x_{2},y_{2})\\), and it satisfies \\(x_{1}^{2}+x_{2}^{2}=\dfrac{21}{2}x_{1}x_{2}\\). Find the equation of line \\(l\\).

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