
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) Suppose $a, b \in (-\infty, 0)$, if $a > b$, then $a - \frac{1}{a} > b - \frac{1}{b}$;
(2) For real numbers $a$ and $b$, if $b(b - a) \leqslant 0 (b \neq 0)$, then $\frac{a}{b} \geqslant 1$. Conversely, if $\frac{a}{b} \geqslant 1$, then $b(b - a) \leqslant 0$;
(3) If $a + c > b + d$, then $a > b$ and $c > d$.
Identify the correct proposition(s) by their number(s).

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