
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 $p$ states that the function $y=(c-1)x+1$ is strictly increasing on $\mathbb{R}$; Proposition $q$ states that the solution set of the inequality $x^{2}-x+c\leqslant 0$ is $\emptyset$. If both propositions $p$ and $q$ are true, find the range of values for the real number $c$.

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