
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
Let $S$ and $V$ represent area and volume, respectively. If the area of triangle $ABC$ is represented as $S_{\triangle ABC}$, and the volume of tetrahedron $O-ABC$ is represented as $V_{O-ABC}$. For the proposition: if $O$ is a point on line segment $AB$, then $| \overset{→}{OB}|· \overset{→}{OA}+| \overset{→}{OA}|· \overset{→}{OB}= \overset{→}{0} $. The planar analogy is: if $O$ is a point within $\triangle ABC$, then ${S}_{\triangle OBC}· \overset{→}{OA}+{S}_{\triangle OCA}· \overset{→}{OB}+{S}_{\triangle OBA}· \overset{→}{OC}= \overset{→}{0} $. The spatial analogy should be: if $O$ is a point within tetrahedron $A-BCD$, then \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

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