
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 incorrect?

1. If the inverse of a proposition is true, then its negation is also necessarily true.
2. The negation of the proposition "For all $x$ in $\mathbb{R}$, $x^2 - x \leq 0$" is "There exists an $x$ in $\mathbb{R}$ such that $x^2 - x \geq 0$".
3. The inverse proposition of "The diagonals of a rectangle are equal" is a true statement.
4. "$x \neq 3$" is a sufficient condition for "|x| \neq 3$ to hold.

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