
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 two complex numbers $z_1 = a_1 + b_1i$ and $z_2 = a_2 + b_2i$ (where $a_1, b_1, a_2, b_2$ are real numbers and $z_1 \neq 0$, $z_2 \neq 0$), determine the condition under which their corresponding vectors lie on the same straight line.

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