
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
If there are three distinct points A, B, and C on line $l$, such that the equation in $x$, $x^2 \overrightarrow{OA} + x \overrightarrow{OB} + \overrightarrow{BC} = \overrightarrow{0}$ ($x \in \mathbb{R}$), has a solution (point O is not on line $l$), then the solution set of this equation is __________.

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