
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
(1) Let $A=\{ x|x^{2}-8x+15=0\}$, $B=\{ x|ax-1=0\}$. If $B \subseteq A$, then the set of real numbers $a$ that make up set $C$ is \_\_\_\_\_\_.

(2) The function $f(x)=\begin{cases} ax^{2}+x-1 & (x > 2) \\ -x+1 & (x\leqslant 2) \end{cases}$ is a monotonically decreasing function on $\mathbb{R}$, then the range of real numbers $a$ is \_\_\_\_\_\_.

(3) Given that the function $f(x)$ is an odd function defined on $\mathbb{R}$, and when $x > 0$, $f(x)=2^{x}-1$, then the value of $f(f(-1))$ is \_\_\_\_\_\_.

(4) The line $l: \begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$ (where $t$ is a parameter) intersects with the circle $C: (x+6)^{2}+y^{2}=25$ at points $A$ and $B$, and $|AB| = \sqrt{10}$, then the slope of line $l$ is \_\_\_\_\_\_.

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