
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
Let proposition \\(p:\\) be the inequality about \\(a\\) that \\(\forall {x} \in \mathbb{R}, {x}^{2} - 4x + {a}^{2} > 0\\); proposition \\(q:\\) be that the quadratic equation in \\(x\\), \\({x}^{2} + (a+1)x + a - 1 = 0\\), has one root greater than zero and the other less than zero; proposition \\(r:\\) be the solution set of \\({a}^{2} - 2a + 1 - {m}^{2} \geqslant 0 (m > 0)\\).

\\((1)\\) If \\(p \vee q\\) is true and \\(p \wedge q\\) is false, find the range of real numbers \\(a\\).

\\((2)\\) If \\(\neg r\\) is a necessary but not sufficient condition for \\(\neg p\\), find the range of real numbers \\(m\\).

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