
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
In a right tetrahedron \(ABCD\), \(DA\), \(DB\), and \(DC\) are mutually perpendicular. Let \(S\) and \(R\) represent its surface area and the radius of the circumscribed sphere, respectively. What is the maximum value of \(\frac{S}{R^2}\)?

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