
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
(1) Given a function $f(x) = x^3 - mx^2 - nx$ whose graph is tangent to the x-axis with the point of tangency at $(1, 0)$, and let $g(x) = f(x) + 1$, find the extreme values of $g(x)$.
(2) Given $f(x) = ax^2 + bx + c$ ($a \neq 0$), and $f(-1) = 2$, $f'(0) = 0$, $\int_{-1}^{0} f(x) \, dx = -4$, determine the values of $a$, $b$, and $c$.

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