
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 set $A=\{x|x^{2}-6x+8\leqslant 0\}$, function $f(x)=a^{x}$ where $a > 0$ and $a\neq 1$, and $x\in A$.
1. If $a=2$, find the minimum and maximum values of $f(x)$.
2. If the difference between the maximum and minimum values of $f(x)$ is $2$, find the value of $a$.

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