
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
Two circles with radius one are drawn in the coordinate plane, one with center \((0,1)\) and the other with center \((2, y)\), for some real number \(y\) between 0 and 1. A third circle is drawn so as to be tangent to both of the other two circles as well as the \(x\)-axis. What is the smallest possible radius for this third circle?

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