
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
Identify the true statements from the following propositions (Write down the numbers of all correct propositions):

① There exists an $x_0 \in \mathbb{R}$ such that $e^{x_0} \leq 0$  
② For all $x \in \mathbb{R}$, $2^x > x^2$  
③ If $a > 1$ and $b > 1$, then it is a sufficient condition for $ab > 1$   
④ $b = \sqrt{ac}$ is neither a sufficient nor a necessary condition for $a, b, c$ to form a geometric sequence.

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