
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
Which of the following judgments are correct? Fill in the correct serial numbers.  
(1) Correspondence: $t \rightarrow s$, where $s=t^2$, $t \in \mathbb{R}$, $s \in \mathbb{R}$, this correspondence is a function;  
(2) The function $y=|x-1|$ and $y= \begin{cases} x-1, & x>1 \\ 1-x, & x<1 \end{cases}$ are the same function;  
(3) If the function $f(x)$ is increasing in the interval $(-\infty, 0)$ and is also increasing in the interval $[0, +\infty)$, then the function $f(x)$ must be increasing on $\mathbb{R}$;  
(4) $A=\{x|x^2+x-6=0\}$, $B=\{x|mx+1=0\}$, and $A \cup B = A$, then the set of values for $m$ is $\left\{-\frac{1}{2}, \frac{1}{3}\right\}$;  
(5) For a function $f(x)$ defined on $\mathbb{R}$ that satisfies $f(2) > f(1)$, then the function $f(x)$ is not a monotonically decreasing function on $\mathbb{R}$;  
(6) The graph of the function $y=f(2x-1)$ can be obtained by shifting the graph of $y=f(2x)$ to the right by 1 unit.

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