
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
Find the domain of the following functions:  
(1) $f(x)= \dfrac {\sqrt {x+1}}{x-2}$;  
(2) $f(x)= \sqrt {1-\left( \dfrac {1}{3}\right)^{x}}$;  
(3) $f(x)= \dfrac {1}{ \sqrt {\log _{2}(x-1)}}$.

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