
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 following four judgments, the correct judgment is ______  
\\((1)\\) If "either \\(p\\) or \\(q\\)" is true, then both \\(p\\) and \\(q\\) are true statements.  
\\((2)\\) The contrapositive of the statement "If \\(x \geqslant 4\\) and \\(y \geqslant 2\\), then \\(x+y \geqslant 6\\)" is "If \\(x+y < 6\\), then \\(x < 4\\) and \\(y < 2\\)".  
\\((3)\\) If \\(x \neq 300^{\circ}\\), then \\(\cos x \neq \frac{1}{2}\\).  
\\((4)\\) The statement "There exists \\(x_{0} \in \mathbb{R}\\) such that \\(e^{x_{0}} \leqslant 0\\)" is false.

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