
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 $a$ and $b$ be the two distinct zeros of the function $f(x)=x^{2}-px+q$, where $p > 0$ and $q > 0$. If $a$, $b$, and $-2$ can be arranged in an arithmetic progression and a geometric progression, find the value of $p+q$. Additionally, consider the point $A$ with coordinates $(p,q)$, the curve $C$ with equation $y= \sqrt {1-x^{2}}$, and the line $l$ passing through $A$ and intersecting curve $C$ at only one point. Find the range of possible slopes for line $l$.

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