
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 function \(f(x)\), if there exists an interval \(A=[m,n]\) such that \(\{y|y=f(x),x\in A\}=A\), then the function \(f(x)\) is called a "same-domain function," and the interval \(A\) is called a "same-domain interval" for the function \(f(x)\). Consider the following four functions:  
\(①f(x)=\cos \frac {\pi}{2}x\); \(②f(x)=x^{2}-1\); \(③f(x)=|x^{2}-1|\); \(④f(x)=\log _{2}(x-1)\).  
The sequence numbers of the functions that have a "same-domain interval" are __________ (please write down all the correct sequence numbers)

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