
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
A rhombus with sides of unit length has an acute angle of $60^{\circ}$. How many circles are there such that all the vertices of the rhombus are equidistant from the circles? What is the radius of these circles?

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