
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 with 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 $f(x) = 0$ ($x \in \mathbb{R}$).

The correct proposition numbers are.

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