
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]


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Among the following four propositions, the correct one(s) is/are $\boxed{\text{answer}}$
$(①)$ The domain of the function $y=x^{- \frac {3}{2}}$ is ${x|x≠ 0}$;
$(②)$ The solution set of the equation $\lg \sqrt {x-2}=\lg (x-2)$ is ${3}$;
$(③)$ The solution set of the equation $3^{1-x}-2=0$ is ${x|x=1-\log _{3}2}$;
$(④)$ The solution set of the inequality $\lg (x-1) < 1$ is ${x|x < 11}$.

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