
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 two propositions: P: The exponential function $y=(c^2-5c+7)^x$ is monotonically increasing on $\mathbb{R}$; Q: The solution set of the inequality $|x-1|+|x-2c|>1$ is $\mathbb{R}$. If exactly one of P and Q is correct, find the range of values for $c$.

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