
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 $c > 0$, let proposition $p$: the function $y = c^{x}$ 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 "p or q" is true, and "p and q" is false, find the range of values for $c$.

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