
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 four statements:
1. The domain of the function $y=a^{x}$ $(a > 0,a\neq 1)$ is the same as the domain of the function $y=x^{2}$;
2. The function $y=2^{x}$ and the function $y=\log_{3}x$ are inverse functions of each other;
3. The interval of monotonic increase for the function $y=\log_{3}(x^{2}-2x-3)$ is $[1,+\infty)$;
4. The range of the function $y=3^{|x|}$ is $[1,+\infty)$.

Among these, the correct statement(s) is/are __________.

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