
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 point \(O\) be located inside a regular tetrahedron \(ABCD\). \(G\) is the center of the tetrahedron. The line \(OG\) intersects the faces of the tetrahedron at points \(A_1, B_1, C_1, D_1\). Find the value of \(\frac{A_1 O}{A_1 G} + \frac{B_1 O}{B_1 G} + \frac{C_1 O}{C_1 G} + \frac{D_1 O}{D_1 G}\).

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