
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
For the given function $f(x) = 2^x - 2^{-x}$, there are four statements: ① The graph of $f(x)$ is symmetric about the origin; ② $f(\log_2 3) = 2$; ③ $f(x)$ is an increasing function on $\mathbb{R}$; ④ $f(|x|)$ has a minimum value of 0. Among these, the correct statements are. (Write down the numbers of all correct statements)

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