
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 $f(x)=x^{2}+2bx+c$, and $f(1)=f(3)=-1$. Let $a > 0$, the graph of function $f(x)$ is translated to the right by $a$ units and then translated downward by $a^{2}$ units to obtain the graph of function $g(x)$.  
(Ⅰ) If the function $g(x)$ has two zeros $x_{1}$, $x_{2}$, and $x_{1} < 4 < x_{2}$, find the range of values for the real number $a$;  
(Ⅱ) Let a continuous function's range on the interval $[m,n]$ be $[\lambda,\mu]$, if $\dfrac {\mu-\lambda}{n-m} > 8$, then the function is called a "steep function". If the function $g(x)$ is a "steep function" on the interval $[a,2a]$, find the range of values for the real number $a$.

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