
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
Among the following propositions:

1. "If $am^{2} < bm^{2}$," then "If $a < b$," is a necessary and sufficient condition.

2. The negation of "The diagonals of a rectangle are equal" is false.

3. "$x \neq 3$" is a sufficient condition for "$|x| \neq 3$" to hold.

4. "$A \cap B = B$" is a necessary but not sufficient condition for "$A = \emptyset$."

5. The contrapositive of "If $a < b$, then $a+c < b+c$" is "If $a+c > b+c$, then $a > b$"

Identify the incorrect propositions.

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