
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 function $y=\log_{2}(ax^{2}-2x+2)$, its domain is $Q$.  
$(1)$ If $a > 0$ and $[2,3] \cap Q = \varnothing$, find the range of the real number $a$;  
$(2)$ If $[2,3] \subseteq Q$, find the range of the real number $a$.

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