
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
Among the following propositions, the correct proposition numbers are _________________

(1) $|\vec{a} \cdot \vec{b}| = |\vec{a}| \cdot |\vec{b}|$

(2) If $\vec{a} \cdot \vec{b} = 0$, then $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$

(3) If $\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{c}$ and $\vec{b} \neq \vec{0}$, then $\vec{a} = \vec{c}$

(4) $(\vec{a} \cdot \vec{b}) \cdot \vec{c} - (\vec{c} \cdot \vec{a}) \cdot \vec{b} = 0$

(5) If $\vec{a}$ and $\vec{b}$ are non-zero vectors, then $|\vec{a} + \vec{b}| > |\vec{a} - \vec{b}|$ always holds

(6) In $\triangle ABC$, if $A > B$, then it must be that $\sin A > \sin B$

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