
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 centers at points A, B, and C respectively, each with a radius of r, where 1<r<2. The distance between any two centers is 2. If point B is the intersection of circles centered at A and C but lies outside the circle centered at B, and C’ is the intersection of circles centered at A and B but lies outside the circle centered at C, calculate the length of B’C’.

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