
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 that $a > 0$, proposition $p$: The function $y=a^{x}$ is a decreasing function. Proposition $q$: When $x \in [\frac{1}{2}, 2]$, the function $f(x) = x + \frac{1}{x} > \frac{1}{a}$ always holds true. If $p$ or $q$ is a true proposition and $p$ and $q$ are both false propositions, find the range of values for $a$.

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