
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 the propositions p and q where:
- p: The function $y=c^x$ is a decreasing function.
- q: The inequality $x^2 - \sqrt{2}x + c > 0$ holds true for all real numbers $x$.

If the negation of q is true and either 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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