
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 cubic function f(x) = x³ + mx² + nx + p with three zero points a, b, and c, and satisfying f(-1) = f(2) < 0, f(1) = f(4) > 0, determine the range of values for $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$.

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