
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
Given the following propositions:
$(①)$ If $ab > 0$ and $a > b$, then $\frac{1}{a} < \frac{1}{b}$
$(②)$ If $a > |b|$, then $a^{2} > b^{2}$
$(③)$ If $a > b$ and $c > d$, then $a-c > b-d$
$(④)$ If $0 < a < b$ and $m > 0$, then $\frac{a}{b} < \frac{a+m}{b+m}$.
The numbers of the true propositions are: \_\_\_\_\_\_\_\_\_.

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