
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 famous Greek mathematician Apollonius of Perga, in his magnum opus "Conics," presented a well-known geometric problem: Given two points A(-a, 0) and B(a, 0) on a plane, a moving point P satisfies the condition $\frac{|PA|}{|PB|} = λ$ (where a and λ are positive constants, and λ ≠ 1). The trajectory of point P is a circle known as the "Apollonius Circle." Determine the radius of this circle.

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