
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 \\(r(x): \sin x + \cos x > m\\) and \\(s(x): x^2 + mx + 1 > 0\\).

\\((1)\\) If for all \\(x \in \left(\frac{1}{2}, 2\right]\), proposition \\(s(x)\\) always holds, find the range of the real number \\(m\\).

\\((2)\\) If for all \\(x \in \mathbb{R}\\), \\(r(x)\\) and \\(s(x)\\) have exactly one true proposition, find the range of the real number \\(m\\).

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