
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
For lines of the form "$x=ky+b$ ($k,b\in\mathbb{R}$)", consider the following statements: 
1. It may be perpendicular to the $y$-axis;
2. It cannot be perpendicular to the $y$-axis;
3. It may be perpendicular to the $x$-axis;
4. It cannot be perpendicular to the $x$-axis.

Among these, the correct ones are __________ (Fill in the sequence numbers).

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