
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 statements is correct? _______.

(1) If $(2x-1)+i=y-(3-y)i$, where $x\in \mathbb{R}$, $y\in \mathbb{C}\backslash \mathbb{R}$, then it must be $\begin{cases} & 2x-1=y \\ & 1=-(3-y) \end{cases}$;

(2) $2+i > 1+i$;

(3) The points on the imaginary axis represent purely imaginary numbers;

(4) If a number is real, then it has no imaginary part;

(5) If $z= \frac{1}{i}$, then $z^{3}+1$ corresponds to a point in the first quadrant of the complex plane.

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