
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 \( p \) : The function \( y=c' \) is monotonically decreasing on \( \mathbf{R} \), \( q \) : The solution set of the inequality \( x + |x - 2c| > 1 \) is \( \mathbf{R} \). If exactly one of \( p \) and \( q \) is correct, determine the range of values for \( c \).

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