
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 in space \\(A(-2,0,2)\\), \\(B(-1,1,2)\\), \\(C(-3,0,4)\\), let \\( \overrightarrow{a}= \overrightarrow{AB}\\), \\( \overrightarrow{b}= \overrightarrow{AC}\\).
\\((1)\\) Find the cosine of the angle between \\( \overrightarrow{a}\\) and \\( \overrightarrow{b}\\).
\\((2)\\) If the vector \\(k \overrightarrow{a}+ \overrightarrow{b}\\) is perpendicular to \\(k \overrightarrow{a}-2 \overrightarrow{b}\\), find the value of the real number \\(k\\).

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