
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
1. If $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-zero vectors, and $\overrightarrow{a} \parallel \overrightarrow{b}$, then $\overrightarrow{a} + \overrightarrow{b}$ must have the same direction as either $\overrightarrow{a}$ or $\overrightarrow{b}$;
2. If $\overrightarrow{e}$ is a unit vector, and $\overrightarrow{a} \nparallel \overrightarrow{e}$, then $\overrightarrow{a} = |\overrightarrow{a}| \cdot \overrightarrow{e}$;
3. $\overrightarrow{a} \cdot \overrightarrow{a} \cdot \overrightarrow{a} = |\overrightarrow{a}|^{3}$;
4. If $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear, and $\overrightarrow{b}$ and $\overrightarrow{c}$ are collinear, then $\overrightarrow{a}$ and $\overrightarrow{c}$ must be collinear;
5. If there are four points $A$, $B$, $C$, $D$ in a plane, then $\overrightarrow{AC} + \overrightarrow{BD} = \overrightarrow{BC} + \overrightarrow{AD}$ must hold.

The correct propositions are __________ (Fill in the serial numbers).

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