
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 $c > 0$ and $c \neq 1$, let $p$: the function $y=c^{x}$ is monotonically decreasing on $\mathbb{R}$; $q$: the function $f(x)=x^{2}-2cx+1$ is increasing on $\left( \frac {1}{2},+\infty\right)$, if "$p$ and $q$" is false, "$p$ or $q$" is true, find the range of the real number $c$.

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