
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 a quadrangular pyramid \( O A B C D \) with a parallelogram \( A B C D \) as its base. A plane \( \alpha \) intersects the edges \( O A, O B, O C, \) and \( O D \) of the pyramid at points \( A', B', C' \), and \( D' \) respectively. It is known that \( \frac{O A'}{O A}=\frac{1}{a} \), \( \frac{O B'}{O B}=\frac{1}{b} \), \( \frac{O C'}{O C}=\frac{1}{c} \). Find \( \frac{V_{O A B C D}}{V_{O A' B' C' D'}} \).

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