
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 following four propositions:
1. The graph of an odd function must pass through the origin;
2. The graph of an even function must be symmetric about the y-axis;
3. The function $y=x^3+1$ is not an odd function;
4. The function $y=-|x|+1$ is not an even function.

Among these, the correct proposition numbers are. (Fill in all that you think are correct)

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