
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 (the result should be expressed as a set or interval):  
(1) $$y= \frac { \sqrt {x-4}}{|x|-5}$$  
(2) $y=\log_{a}(2-x)$ ($a>0$ and $a\neq 1$)  
(3) $$y= \sqrt {1-\left( \frac {1}{2}\right)^{x}}$$．

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