
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 that the midpoint of the segment cut by the lines $l_1: 2x+y+1=0$ and $l_2: x-2y-3=0$ on line $l$ is exactly the origin of the coordinate system.  
(1) Find the equation of line $l$;  
(2) If there do not exist two points on the parabola $y=ax^2-1$ ($a\neq 0$) that are symmetric about line $l$, find the range of the real number $a$.

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