
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 proposition \\(p\\) be: the function \\(y = c^x\\) is a decreasing function. Proposition \\(q\\) is: when \\(x \in \left[ \frac{1}{2}, 2 \right]\\), the function \\(f(x) = x + \frac{1}{x} > c\\) always holds. If "either \\(p\\) or \\(q\\)" is true, and "both \\(p\\) and \\(q\\)" is false, find the range of values for \\(c\\).

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