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

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