
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:
$(①)$ The function $y=-\frac{1}{x}$ is monotonically increasing on $\mathbb{R}$;

$(②)$ If the function $y=x^{2}+2ax+1$ is monotonically decreasing on $(-∞,-1]$, then $a\leqslant 1$;

$(③)$ If $\log_{0.7}(2m) < \log_{0.7}(m-1)$, then $m < -1$;

$(④)$ If $f(x)$ is an odd function defined on $\mathbb{R}$, then $f(1-x)+f(x-1)=0$.

The correct proposition number(s) is/are _____.

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