
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 propositions $p$ and $q$:
- Proposition $p$: The function $y = c^x$ is a decreasing function.
- Proposition $q$: $x^2 - \sqrt{2}x + c > 0$ holds true for all $x \in \mathbb{R}$.

If $\lnot q$ is true and either $p$ or $q$ is true, find the range of valid values for $c$.

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