
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
Let $t\neq 0$, and point $P(t,0)$ be a common point of the graphs of the functions $f(x)=x^{3}+ax$ and $g(x)=bx^{2}+c$. The graphs of the two functions have the same tangent line at point $P$.  
(I) Express $a$, $b$, and $c$ in terms of $t$;  
(II) If the function $y=f(x)-g(x)$ is monotonically decreasing on the interval $(-1,3)$, find the range of values for $t$.

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