
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
There are four propositions as follows:
1. For a real number $m$ and vectors $\vec{a}, \vec{b}$, we always have $m(\vec{a} - \vec{b}) = m\vec{a} - m\vec{b}$;
2. For real numbers $m, n$ and a vector $\vec{a}$, we always have $(m - n)\vec{a} = m\vec{a} - n\vec{a}$;
3. For a real number $m$ and vectors $\vec{a}, \vec{b}$, if $m\vec{a} = m\vec{b}$, then $\vec{a} = \vec{b}$;
4. For real numbers $m, n$ and a non-zero vector $\vec{a}$, if $m\vec{a} = n\vec{a}$, then $m = n$.

Among these propositions, the true ones are ______________.

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