
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 $c > 0$ and $c \neq 1$, let $p$ be the statement that the function $y = \log_c x$ is monotonically increasing on $(0, +\infty)$, and let $q$ be the statement that the function $f(x) = x^2 - 2cx + 1$ is decreasing on $(-\infty, \frac{1}{2})$. If the statement "$p$ and $q$" is false, while the statement "$p$ or $q$" is true, find the range of values for the real number $c$.

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