
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
Given the following propositions:

1. If two vectors are equal, then their starting points and ending points are the same;
2. If $|a|=|b|$, then $a=b$ or $a=-b$;
3. If $A$, $B$, $C$, $D$ are four non-collinear points, and $\overrightarrow{AB}=\overrightarrow{DC}$, then $ABCD$ is a parallelogram;
4. The necessary and sufficient condition for $a=b$ is $|a|=|b|$ and $a\parallel b$;

Among these, the true proposition(s) is/are __________.

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