
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) = -x^3 + ax^2 + bx + c (a, b, c ∈ R), and f'(-1) = f'(3) = 0.
1. Find the values of a and b.
2. If the maximum value of the function f(x) in the interval [-2, 2] is 20, find its minimum value in this interval.

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