
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 \\(| \overrightarrow{a}|=1\\) and \\(| \overrightarrow{b}|= \sqrt {2}\\),  
\\((1)\\) If \\( \overrightarrow{a}\\) is parallel to \\( \overrightarrow{b}\\), find \\( \overrightarrow{a} \cdot \overrightarrow{b}\\);  
\\((2)\\) If the angle between \\( \overrightarrow{a}\\) and \\( \overrightarrow{b}\\) is \\(60^{\circ}\\), find \\(| \overrightarrow{a}+2 \overrightarrow{b}|\\);  
\\((3)\\) If \\( \overrightarrow{a}- \overrightarrow{b}\\) is perpendicular to \\( \overrightarrow{a}\\), find the angle between \\( \overrightarrow{a}\\) and \\( \overrightarrow{b}\\).

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