
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
Four larger circles with radius 5 are arranged so that their centers are the vertices of a square. Each of the larger circles is tangent to two of the other circles. A smaller circle with radius \( r \) is drawn in the region between the four larger circles, tangent to each of the larger circles. Calculate the value of \( r \).

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