
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 proposition $p$: There exists some $x$ in $\mathbb{R}$ such that $x - 2 > 0$, and the proposition $q$: For all $x$ in $\mathbb{R}$, $\sqrt{x} > x$, determine which of the following statements is true:
1. The proposition $p \lor q$ is false.
2. The proposition $p \land q$ is true.
3. The proposition $p \lor (\neg q)$ is false.
4. The proposition $p \land (\neg q)$ is true.

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