
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 line \\(l_{1}\\): \\(ax+y+2=0(a\in\mathbb{R})\\).
\\((1)\\) If the slope angle of line \\(l_{1}\\) is \\(120^{\circ}\\), find the value of the real number \\(a\\);
\\((2)\\) If the intercept of line \\(l_{1}\\) on the \\(x\\)-axis is \\(2\\), find the value of the real number \\(a\\);
\\((3)\\) If line \\(l_{1}\\) is parallel to line \\(l_{2}\\): \\(2x-y+1=0\\), find the distance between the two parallel lines.

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