
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 $a$, $b$, and $c$, consider the following propositions:
1. "$a=b$" is a necessary and sufficient condition for "$ac=bc$";
2. "$a+5$ is an irrational number" is a necessary and sufficient condition for "$a$ is an irrational number";
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 true propositions are numbered ____.

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