
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
There are the following three statements:
1. The negation of the proposition "There exists an $x \in \mathbb{R}$, such that $x^{2}-x > 0$" is "For all $x \in \mathbb{R}$, $x^{2}-x \leqslant 0$";
2. "The truth of $p \lor q$" is a necessary but not sufficient condition for "The falseness of $\neg p$";
3. When randomly selecting a number from the interval $[0,\pi]$, the probability of the event "$\sin x \geqslant \frac{1}{2}$" occurring is $\frac{5}{6}$.

The number of correct statements is ______.

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