
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 propositions $p$: $A \cap \emptyset = \emptyset$, $q$: $A \cup \emptyset = A$, consider the following statements: (1) $p \land q$ is true; (2) $\neg p \lor \neg q$ is true; (3) $\neg p \lor q$ is true; (4) $\neg p \land q$ is true. Identify the correct statement(s).

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