
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
Three circles have the same center O. Circle A has radius OP, Circle B has radius OX, where X is the midpoint of segment OP, and Circle C is tangent to Circle A externally with its center on the line OP extended and OC = 2OP. Calculate the ratio of the area of Circle B to the total area of Circles A and C.

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