
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 \( p \) be the statement: the function \( y = c^x \) is monotonically decreasing on \( \mathbf{R} \), and \( q \) be the statement: the solution set of the inequality \( x + |x - 2c| > 1 \) is \(\mathbf{R}\). If exactly one of the statements \( p \) and \( q \) is true, find the range of values for \( c \).

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