
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 $a > b$, then $\frac{1}{a} < \frac{1}{b}$;
$(②)$ If $a > b$, and $k \in \mathbb{N}^*$, then $a^{k} > b^{k}$;
$(③)$ If $ac^{2} > bc^{2}$, then $a > b$;
$(④)$ If $\frac{1}{a} > 1$, then $0 < a < 1$.
Determine the true proposition(s) by filling in the sequence number(s).

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