
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 $O$ be any point inside triangle $ABC$. Extend side $AO$ to intersect the opposite side at $A'$, then $\frac{AO}{AA'} = \frac{S_{quadrilateralABOC}}{S_{\triangle ABC}}$. Similarly, extend sides $BO$ and $CO$ to intersect the opposite sides at $B'$ and $C'$, respectively. Deduce the value of $\frac{AO}{AA'} + \frac{BO}{BB'} + \frac{CO}{CC'} = \_\_\_\_\_\_$. Similarly, if $O$ is any point inside tetrahedron $ABCD$, connect $AO$, $BO$, $CO$, $DO$ and extend them to intersect the opposite faces at $A'$, $B'$, $C'$, $D'$, respectively. Deduce the value of $\frac{AO}{AA'} + \frac{BO}{BB'} + \frac{CO}{CC'} + \frac{DO}{DD'} = \_\_\_\_\_\_$.

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