
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 through point $O$, located inside the triangular pyramid $A B C D$, segments $A A_{1}, B B_{1}, C C_{1}, D D_{1}$ are drawn, where $A_{1}$ lies on the face opposite vertex $A$, $B_{1}$ on the face opposite vertex $B$, and so on, the following equality holds:

$$
\frac{A_{1} O}{A_{1} A} + \frac{B_{1} O}{B_{1} B} + \frac{C_{1} O}{C_{1} C} + \frac{D_{1} O}{D_{1} D} = 1
$$

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