
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 $c$ be a real number greater than $0$. Proposition $p$: $y=c^{x}$ is a decreasing function. Proposition $q$: When $x \in \left[\frac{1}{2},2\right]$, the function $f(x)=x+\frac{1}{x} > \frac{1}{c}$ always holds. If either $p$ or $q$ is true, but not both, find the range of values for $c$.

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