
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
Define a tetrahedron with all its edges of equal length as an isosceles tetrahedron. Let \( DBMN \) be an isosceles tetrahedron with its circumscribed sphere radius being \( R \) and the circumcircle radius of \( \triangle BMN \) being \( r \). Given
\[ DB = MN = a, \quad DM = BN = b, \quad DN = BM = c, \]
determine the range of values for \( \frac{r}{R} \).

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