
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 proposition \\(p\\): There exists \\(x_{0} \in \mathbb{R}\\) such that \\(\sin x_{0} = \frac{\sqrt{5}}{2}\\); proposition \\(q\\): For all \\(x \in \mathbb{R}\\), \\(x^{2} + x + 1 > 0\\). The following conclusions are given: \\(①\\) The proposition "\\(p \land q\\)" is true; \\(②\\) The proposition "\\(p \land (\neg q)\\)" is false; \\(③\\) The proposition "\\((\neg p) \lor q\\)" is true; \\(④\\) The proposition "\\((\neg p) \lor (\neg q)\\)" is false. Among these, the correct ones are __________ (Fill in all the correct conclusion numbers).

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