
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
Consider the following four statements:  
(1) The function $y=a^x \ (a>0, a\neq 1)$ has the same domain as the function $y=x^2$;  
(2) The function $y=2^x$ is the inverse function of $y=\log_3 x$;  
(3) The function $y=\log_3 (x^2-2x-3)$ is monotonically increasing in the interval $[1, +\infty)$;  
(4) The function $y=3^{|x|}$ has a range of $[1, +\infty)$.  
Indicate all the correct statement numbers.

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