
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 propositions:  
① The negation of the proposition "There exists an $x \in \mathbb{R}$ such that $x^2 - x > 0$" is "For all $x \in \mathbb{R}$, $x^2 - x \le 0$";  
② The inverse of the proposition "If $am^2 < bm^2$, then $a < b$" is true;  
③ If $f(x)$ is an odd function defined on $(-\infty, 0) \cup (0, +\infty)$, and the analytic expression for $x > 0$ is $f(x) = 2^x$, then the analytic expression for $x < 0$ is $f(x) = -2^{-x}$;  
④ If the random variable $\xi \sim N(1, \sigma^2)$, and $P(0 \le \xi \le 1) = 0.3$, then $P(\xi \ge 2) = 0.2$.  
Among these propositions, the numbers of the true propositions are ____. (Write down all the numbers of propositions you believe are correct).

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