
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
Fourteen spheres each with a radius of 2 are placed within the first quadrant, each tangent to the three coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these fourteen spheres?
A) $2\sqrt{3} + 2$
B) $2\sqrt{3} + 4$
C) $4\sqrt{3} + 4$
D) $4\sqrt{3} + 2$

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