
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 points \( A, B, \) and \( C \) are pairwise \( d \) distance apart. By drawing circles centered at each of these points with radius \( d \) (in the plane they determine), consider the arc-triangle \( ABC \). Construct three circles within this arc-triangle that pairwise touch each other and each touch two sides of the arc-triangle.

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