
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
Which of the following propositions about space vectors are correct?  
① If vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ cannot form a basis with any vector in space, then $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$.  
② If non-zero vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ satisfy $\overrightarrow{a} \perp \overrightarrow{b}$, $\overrightarrow{b} \perp \overrightarrow{c}$, then $\overrightarrow{a}$ is parallel to $\overrightarrow{c}$.  
③ If $\overrightarrow{OA}$, $\overrightarrow{OB}$, $\overrightarrow{OC}$ are a set of basis vectors in space, and $\overrightarrow{OD} = \frac{1}{3}\overrightarrow{OA} + \frac{1}{3}\overrightarrow{OB} + \frac{1}{3}\overrightarrow{OC}$, then points $A$, $B$, $C$, and $D$ are coplanar.  
④ If vectors $\overrightarrow{a} + \overrightarrow{b}$, $\overrightarrow{b} + \overrightarrow{c}$, $\overrightarrow{c} + \overrightarrow{a}$ form a set of basis vectors in space, then vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ also form a set of basis vectors in space.

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