
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
\[
a + b + c + d = 10,
\]
\[
a^2 + b^2 + c^2 + d^2 = 30.
\]
Let \( m \) and \( M \) denote the minimum and maximum values of
\[
4(a^3 + b^3 + c^3 + d^3) - 3(a^2 + b^2 + c^2 + d^2)^2.
\]
Find \( m + M \).

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