
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 $p$: the function $y=c^x$ is monotonically decreasing on $\mathbb{R}$; $q$: the function $g(x)=\lg(2cx^2+2x+1)$ has domain $\mathbb{R}$. If the statement "p and q" is false, and "p or q" is true, find the range of values for $c$.

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