
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 proposition _\\(p\\)_: \\(f(x) = \log_2(x^2 - 2mx + \frac{1}{2})\\) is monotonically increasing for \\(x \in [1, +\infty)\\); proposition _\\(q\\)_: the equation \\(x^2 - mx - 2 = 0\\) has a solution for \\(x \in [0,1]\\); if the negation of _\\(q\\)_ is true, and the disjunction of _\\(p\\)_ and _\\(q\\)_ is true, then the range of the real number \\(m\\) is \_\_\_\_\_\_.

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