
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 quadratic function $f(x)=x^{2}-16x+q+3$:
(1) Find the range of values for the real number $q$ such that the function has zero points in the interval $[-1,1]$;
(2) Determine if there exists a constant $t(t\geqslant 0)$, such that when $x\in[t,10]$, the range of $f(x)$ is the interval $D$, and the length of $D$ is $12-t$.

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