
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
The radii of two non-overlapping spheres are $R$ and $r$; the distance between their centers is $a$. What are the possible lengths that a common tangent to these spheres can be?

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