
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:
① The condition $|\vec{a}| + |\vec{b}| = |\vec{a} + \vec{b}|$ is a necessary and sufficient condition for vectors $\vec{a}$ and $\vec{b}$ to be collinear;
② For any point $O$ in space and three non-collinear points $A$, $B$, and $C$, if $\vec{OP} = 2\vec{OA} + 3\vec{OB} - 4\vec{OC}$, then points $P$, $A$, $B$, and $C$ are coplanar;
③ If the normal vectors of two planes are not perpendicular, then these two planes are definitely not perpendicular.
The correct proposition(s) is/are __________.

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