
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 $f(x)=x^{2}-16x+q+3$:  
$(1)$ If the minimum value of the function is $-60$, find the value of the real number $q$;  
$(2)$ If the function has a root in the interval $[-1,1]$, find the range of values for the real number $q$.

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