
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
A unit cube is packed with spheres such that one sphere's center is at one vertex of the cube, and it fits perfectly such that each sphere touches exactly three faces of the cube and is tangent to its six neighboring spheres. Calculate the radius of each sphere.
A) \(\frac{1}{4}\)
B) \(\frac{\sqrt{3}}{4}\)
C) \(\frac{\sqrt{2}-1}{4}\)
D) \(\frac{\sqrt{3}(3-\sqrt{3})}{4}\)
E) \(\frac{\sqrt{3}(\sqrt{3}-1)}{4}\)

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