
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 triangle  $\vartriangle ABC$  has  $\angle B = 90^o$  . A circle is tangent to  $AB$  at  $B$  and also tangent to  $AC$ . Another circle is tangent to the first circle as well as the two sides  $AB$  and  $AC$ . Suppose that  $AB =\sqrt3$  and  $BC = 3$ . What is the radius of the second circle?

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