
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 with centers $A$, $B$, and $C$ each have radii, $r_A = 2$, $r_B = r_C = 1.5$. The centers $A$, $B$, and $C$ form an equilateral triangle with each side length equal to $3$. Find the length of line segment $B'C'$, where $B'$ is the intersection of the circle centered at $A$ and the circle centered at $B$ that is outside the circle centered at $C$, and $C'$ is the intersection of the circle centered at $A$ and the circle centered at $C$ that is outside the circle centered at $B$.
A) $\sqrt{5}$
B) $\sqrt{8}$
C) $3$
D) $2.5$

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