
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 the universal set $U=\{1,2\}$, and the set $A=\{x|x^2+px+q=0\}$, $C_UA=\{1\}$,  
(1) Find $p$ and $q$;  
(2) Try to find the inverse function of $y=px^2+qx+15$ on the interval $\left[\frac{1}{2}, 2\right]$.

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