
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°, find the value of the real number $a$;  
(2) If the x-intercept of line $l_1$ 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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