
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 circle with a radius of \( r \) is touched by four other circles, each also with a radius of \( r \), and no two of these circles have interior points in common. What is the radius of the smallest circle that can contain all of these circles?

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