
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
In space, there are four spheres with radii of 2, 2, 3, and 3. Each sphere is externally tangent to the other three spheres. There is an additional small sphere that is externally tangent to all four of these spheres. Find the radius of this small sphere.

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