
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
In a rectangular prism with dimensions 2 units by 2 units by 4 units, eight congruent spheres are packed in such a way that each sphere is tangent to two of the 2-unit faces and one of the 4-unit faces. Additionally, each sphere is tangent to either three or four of its neighboring spheres depending on its position within the prism. What is the radius of each sphere?
A) $\frac{1}{4}$
B) $\frac{\sqrt{2}}{4}$
C) $\frac{1}{2}$
D) $\frac{\sqrt{3}}{4}$

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