
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
Each vertex of the parallelogram $ABCD$ lies on the same side of the plane $S$ such that the distances of the vertices $A, B$, and $C$ from the plane $S$ are 4 cm, 6 cm, and 8 cm, respectively. The area of the projection of the parallelogram onto the plane $S$, which forms the quadrilateral $A'B'C'D'$, is $10 \text{ cm}^2$. What is the volume of the solid $ABCD A'B'C'D'$?

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