
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
Which of the following statements is correct? Enter the serial number \_\_\_\_\_\_\_\_\_\_\_\_.

(1) For two non-coincident straight lines, "the slopes of two straight lines being equal" is a necessary but not sufficient condition for "the two straight lines being parallel";
(2) The negation of the proposition "For all \(x\) in \(\mathbb{R}\), \(\sin x \leqslant 1\)" is "There exists an \(x_0\) in \(\mathbb{R}\) such that \(\sin x_0 > 1\)";
(3) "Both \(p\) and \(q\) are true" is a sufficient but not necessary condition for "Either \(p\) or \(q\) is true";
(4) Given two straight lines \(a, b\) and a plane \(\alpha\), if \(a \perp \alpha\) and \(b \parallel \alpha\), then \(a \perp b\).

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