
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’s consider a hypercube (or 4-cube or tesseract) in four-dimensional space with side length 1. Three vertices of a 4-simplex within this tesseract are given as points \( (0,0,0,0) \), \( (1,1,0,0) \), \( (1,0,1,0) \), and \( (1,0,0,1) \), and \( (0,1,1,1) \). Calculate the ratio of the hypervolume of the tesseract to the hypervolume of the 4-simplex.
A) \( \frac{12}{\sqrt{5}} \)  
B) \( \frac{24}{\sqrt{5}} \)  
C) \( \frac{48}{\sqrt{5}} \)  
D) \( 5 \sqrt{5} \)

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