
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 $f(x)=x^{3}-2ax^{2}+bx+c$,  
$(1)$ When $c=0$, the tangent line of $f(x)$ at point $P(1,3)$ is parallel to the line $y=x+2$, find the values of $a$ and $b$;  
$(2)$ If $f(x)$ has extreme values at points $A(-1,8)$ and $B(3,-24)$, find the expression of $f(x)$.

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