
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 set $A=\{x|x^{2}-8x+15=0\}$, and the set $B=\{x|ax-1=0\}$.

$(1)$ If $a= \frac{1}{5}$, determine the relationship between set $A$ and set $B$;

$(2)$ If $B \subseteq A$, find the set of real numbers $a$.

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