
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 base of the pyramid \(ABCD\) is the triangle \(ABC\) with sides \(AC=6\), \(BC=8\), \(AB=10\). All the lateral edges are equal to \(5\sqrt{2}\). Find a) the radius of the circumscribed sphere around the pyramid \(ABCD\); b) the distance between the lines \(DM\) and \(AC\) and the distance between the lines \(DM\) and \(BC\), where \(DM\) is the altitude of the pyramid \(ABCD\).

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