
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 sets $A=\{x|x^{2}-8x+15=0\}$ and $B=\{x|ax-1=0\}$.
(1) If $a=\frac{1}{5}$, determine the relationship between set $A$ and set $B$;
(2) If $A \cap B = B$, find the set $C$ composed of all possible real values of $a$.

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