
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 the proposition \\(p: \exists x \in \mathbb{R}, x^2 + 2x - m - 1 < 0\\),

\\((1)\\) Write the negation of proposition \\(p\\);

\\((2)\\) Find the range of the real number \\(m\\) when proposition \\(p\\) is true.

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