
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^x\\) is monotonically decreasing on \\(R\\); \\(q:\\) the solution set of the inequality \\(x^2 + x + \frac{1}{2}c > 0\\) is \\(R\\). If \\(p\\) or \\(q\\) is true, and both \\(p\\) and \\(q\\) are false, find the range of the real number \\(c\\).

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