
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 three points \\(A\\), \\(B\\), and \\(C\\) on a plane satisfying \\( \overrightarrow{BC}=(2-k,3)\\) and \\( \overrightarrow{AC}=(2,4)\\):
\\((1)\\) If points \\(A\\), \\(B\\), and \\(C\\) cannot form a triangle, find the condition that the real number \\(k\\) must satisfy;
\\((2)\\) If \\(\triangle ABC\\) is a right-angled triangle, find the value of the real number \\(k\\).

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