
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
In the set of real numbers $\mathbb{R}$, we define a "sequence" relationship denoted by “＞”. Similarly, we can also define a "sequence" relationship in the complex number set $\mathbb{C}$, denoted as “＞”. The definition is as follows: For any two complex numbers $z_1=a_1+b_1i$, $z_2=a_2+b_2i$ ($a_1$, $b_1$, $a_2$, $b_2 \in \mathbb{R}$, $i$ is the imaginary unit), “$z_1＞z_2$” if and only if “$a_1＞a_2$” or “$a_1=a_2$ and $b_1＞b_2$”. Among the following propositions, the false one is (fill in all the numbers that apply):  
① $1＞i＞0$  
② If $z_1＞z_2$, $z_2＞z_3$, then $z_1＞z_3$  
③ If $z_1＞z_2$, then for any $z \in \mathbb{C}$, $z_1+z＞z_2+z$  
④ For a complex number $z＞0$, if $z_1＞z_2$, then $z \cdot z_1＞z \cdot z_2$.

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