
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
Two equal triangles $KLM$ and $KLN$ share a common side $KL$, with $\angle KLM = \angle LKN = 60^\circ$, $KL = 1$, and $LM = KN = 6$. The planes of $KLM$ and $KLN$ are perpendicular. Find the radius of the sphere that touches the segments $LM$ and $KN$ at their midpoints.

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