
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 $f(x)=ax^{3}+bx+c (a\ne 0)$ as an odd function, its graph's tangent line at the point $(1,f(1))$ is perpendicular to the line $x+18y-7=0$, and the derivative function $f'''(x)$ has a minimum value of $12$.

(1) Find the values of $a$, $b$, and $c$.
(2) Let $g(x)=\frac{f(x)}{x^{2}}$, find the minimum value of $g(x)$ when $x > 0$.

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