
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 $f(x)= \frac {1}{3}x^{3}+ \frac {1}{2}x^{2}-2x+a$, its graph intersects the $y$-axis at a point where the equation of the tangent line is $y=bx+1$.

(I) Find the values of the real numbers $a$ and $b$.
(II) If the function $g(x)=f(x)+ \frac {1}{2}(m-1)x^{2}-(2m^{2}-2)x-1$ has a minimum value of $- \frac {10}{3}$, find the value of the real number $m$.
(III) If for any $x_{1}$, $x_{2}∈[-1,0]$ ($x_{1}≠ x_{2}$), the inequality $|f(x_{1})-f(x_{2})|≥ t|x_{1}-x_{2}|$ always holds, find the range of values for the real number $t$.

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