
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
If point $O$ is inside $\Delta ABC$, then there is a conclusion $({S_{\Delta OBC}} \cdot \overrightarrow{OA} + {S_{\Delta OAC}} \cdot \overrightarrow{OB} + {S_{\Delta OAB}} \cdot \overrightarrow{OC} = \overrightarrow{0})$. Extend this proposition to three dimensions: if point $O$ is inside the tetrahedron $ABCD$, what conclusion can be drawn?

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