
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, \text{ and } c \neq 1\\), let proposition \\(p\\) be: the exponential function \\(y = c^x\\) is a decreasing function; proposition \\(q\\) be: the equation in \\(x\\), \\(x^2 + 2\sqrt{c}x + \frac{1}{2} = 0\\), has two distinct real roots. If "proposition \\(p\\) or proposition \\(q\\)" is true, and "proposition \\(p\\) and proposition \\(q\\)" is false, find the range of the real number \\(c\\).

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