
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
Define a function $f(x)$ on $(-\infty, 0) \cup (0, +\infty)$, if for any given geometric sequence $\{a_n\}$, $\{f(a_n)\}$ is still a geometric sequence, then $f(x)$ is called a "geometric function". Now, consider the following functions defined on $(-\infty, 0) \cup (0, +\infty)$:  
① $f(x) = 2^x$;  
② $f(x) = \log_2|x|$;  
③ $f(x) = x^2$;  
④ $f(x) = \ln 2^x$,  
then the serial numbers of the "geometric functions" among these $f(x)$ are.

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