
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
Given the proposition:

If point $O$ is on line segment $AB$, then $|$\overrightarrow{OB}$|$·$$\overrightarrow{OA}$ + $|$\overrightarrow{OA}$|$·$$\overrightarrow{OB}$ = 0$.

When extended to a planar situation, it becomes:

If point $O$ is inside $△ABC$, then $S_{△OBC}$·$$\overrightarrow{OA}$ + $S_{△OCA}$·$$\overrightarrow{OB}$ + $S_{△OAB}$·$$\overrightarrow{OC}$ = 0$.

Extend this to a spatial situation:

If point $O$ is inside tetrahedron $ABCD$, then \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

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