
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
Evaluate or simplify:  
 \\((1)\\dfrac{\\sqrt{1-2\\sin {15}^{\\circ}\\cos {15}^{\\circ}}}{\\cos {15}^{\\circ}-\\sqrt{1-\\cos^2 {165}^{\\circ}}}\\)；  
 \\((2)\\)Given \\(| \\vec{a} |=4\\), \\(| \\vec{b} |=2\\), and the angle between \\(\\vec{a}\\) and \\(\\vec{b}\\) is \\(\\dfrac{2\\pi }{3}\\), find the value of \\(| \\vec{a} + \\vec{b} |\\).

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