
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 $f(x)=x^{3}+ax^{2}+bx+c$ which attains its minimum value of $-5$ at $x\_0$, and its derivative $y=f′(x)$ passes through the points $(0,0)$ and $(2,0)$.
(1) Find the values of $a$ and $b$;
(2) Find $x\_0$ and the expression of the function $f(x)$.

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