
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 $R$, we define a "sequence" through the relation "$>$" among all real numbers. Similarly, we can also define a "sequence" relation on the set of plane vectors $D=\{ \overrightarrow{a}| \overrightarrow{a}=(x,y), x\in R, y\in R\}$, denoted as "$›$". The definition is as follows: For any two vectors $\overrightarrow{a_{1}}=(x_{1},y_{1})$, $\overrightarrow{a_{2}}=(x_{2},y_{2})$, $\overrightarrow{a_{1}}› \overrightarrow{a_{2}}$ if and only if "$x_{1} > x_{2}$" or "$x_{1}=x_{2}$ and $y_{1} > y_{2}$". According to the relation "$›$" defined above, the following four propositions are given:  
(1) If $\overrightarrow{e_{1}}=(1,0)$, $\overrightarrow{e_{2}}=(0,1)$, $\overrightarrow{0}=(0,0)$, then $\overrightarrow{e_{1}}› \overrightarrow{e_{2}}› \overrightarrow{0}$;  
(2) If $\overrightarrow{a_{1}} > \overrightarrow{a_{2}}$, $\overrightarrow{a_{2}} > \overrightarrow{a_{3}}$, then $\overrightarrow{a_{1}} > \overrightarrow{a_{3}}$;  
(3) If $\overrightarrow{a_{1}} > \overrightarrow{a_{2}}$, then for any $\overrightarrow{a}\in D$, $( \overrightarrow{a_{1}}+ \overrightarrow{a}) > ( \overrightarrow{a_{2}}+ \overrightarrow{a})$;  
(4) For any vector $\overrightarrow{a} > \overrightarrow{0}$, $\overrightarrow{0}=(0,0)$ if $\overrightarrow{a_{1}} > \overrightarrow{a_{2}}$, then $\overrightarrow{a}\cdot \overrightarrow{a_{1}} > \overrightarrow{a}\cdot \overrightarrow{a_{2}}$.  
The sequence numbers of the true propositions are $\boxed{\text{①②③}}$.

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