
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
Three lines on a plane, $x + 2y - 1 = 0$, $x + 1 = 0$, and $x + ky = 0$, divide the plane into six parts. The value(s) of the real number $k$ is/are \_\_\_. (Fill in all correct options) ①0; ②; ③1; ④2; ⑤3.

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