
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
Among the following propositions, the true one is marked by \_\_\_\_\_\_.
\\((1)\\) The negation of the proposition "For all \\(x > 0\\), \\(x^{2}-x \leqslant 0\\)" is "There exists an \\(x > 0\\) such that \\(x^{2}-x > 0\\)."
\\((2)\\) If \\(A > B\\), then \\(\sin A > \sin B\\).
\\((3)\\) Given a sequence \\(\{a_{n}\}\\), "The sequence \\(a_{n}\\), \\(a_{n+1}\\), \\(a_{n+2}\\) forms a geometric sequence" is a necessary and sufficient condition for "\\(a_{n+1}^{2} = a_{n}a_{n+2}\\)."
\\((4)\\) Given the function \\(f(x) = \lg x + \frac{1}{\lg x}\\), the minimum value of the function \\(f(x)\\) is \\(2\\).

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