
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
Let $a,$ $b,$ $c,$ $d$ be real numbers such that
\[
a + b + c + d = 10, \quad a^2 + b^2 + c^2 + d^2 = 30.
\]
Determine the minimum and maximum values of
\[
S = 3(a^3 + b^3 + c^3 + d^3) - 3a^2 - 3b^2 - 3c^2 - 3d^2.
\]

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