
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
Given the function f(x) = $\frac{1}{3}$x^3^ + $\frac{1−a}{2}$x^2^ - ax - a, x ∈ R, where a > 0.
(1) Find the monotonic intervals of the function f(x);
(2) If the function f(x) has exactly two zeros in the interval (-3, 0), find the range of values for a;
(3) When a = 1, let the maximum value of the function f(x) on the interval [t, t+3] be M(t), and the minimum value be m(t). Define g(t) = M(t) - m(t), find the minimum value of the function g(t) on the interval [-4, -1].

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