
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 $p$: $y=c^x$ is monotonically decreasing on $\mathbb{R}$, and $q$: the range of $g(x)=\ln(2cx^2-2x+1)$ is $\mathbb{R}$. If the statement "¬p or ¬q" is true, and the statement "p or q" is also true, then the range of the real number $c$ is \_\_\_\_\_\_.

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