
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
Among the following four propositions: 
1. The graph of an even function must intersect the y-axis.
2. The graph of an odd function must pass through the origin.
3. The graph of an even function is symmetric about the y-axis.
4. A function that is both odd and even must be $f(x)=0$ for all $x \in \mathbb{R}$.

The correct proposition number(s) is/are.

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