
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
Three identical cylindrical surfaces with radius $R$ have mutually perpendicular axes and touch each other pairwise.

a) What is the radius of the smallest sphere that touches these cylindrical surfaces?

b) What is the radius of the largest cylinder that touches the three given cylinders, if its axis passes inside the triangle with vertices at the points of contact of the three given cylinders?

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