
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 four propositions:
- (1) If $a > b$ and $c > d$, then $a-d > b-c$;
- (2) If $a > b$ and $c > d$, then $ac > bd$;
- (3) If $a > b$, then $\dfrac{1}{a-b} > \dfrac{1}{a}$;
- (4) If $\dfrac{1}{a} < \dfrac{1}{b} < 0$, then $ab < b^{2}$.

Among these, the true propositions are __________ (Fill in the serial numbers).

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