
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 equation \\(C\\) about \\(x\\) and \\(y\\): \\(x^{2}+y^{2}-2x-4y+m=0\\).
\\((1)\\) If equation \\(C\\) represents a circle, find the range of values for \\(m\\);
\\((2)\\) If circle \\(C\\) is tangent to the circle \\(x^{2}+y^{2}-8x-12y+36=0\\), find the value of \\(m\\);
\\((3)\\) If circle \\(C\\) intersects line \\(l\\): \\(x+2y-4=0\\) at points \\(M\\) and \\(N\\), and \\(|MN|= \dfrac {4 \sqrt {5}}{5}\\), find the value of \\(m\\).

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