
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
There are four mutually tangent spheres with equal radii. Imagine a fifth sphere which touches the four spheres. Calculate the ratio of the radius of the fifth sphere to the radius of one of the given spheres.

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