
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
For any real numbers $a$, $b$, $c$, consider the following propositions:  
① "a=b" is a necessary and sufficient condition for "ac=bc";  
② "a+5 is irrational" is a necessary and sufficient condition for "a is irrational";  
③ "a>b" is a sufficient condition for "a^2>b^2";  
④ "a<5" is a necessary condition for "a<3".  
Among these, the number of false propositions is.

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