
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 parabola \( y = ax^2 \), and lines \( l_1 \) and \( l_2 \) both passing through the point \( (1, -2) \) and perpendicular to each other, determine the range of the real number \( a \) if the parabola intersects at least one of the lines \( l_1 \) or \( l_2 \).

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