
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 inequality $x^{2}-2ax+a \gt 0$ holds for any real number $x$.  
$(1)$ Find the range of values for $a$;  
$(2)$ Find the solution set for the inequality ${a}^{x^{2}-3}＜{a}^{2x}＜1$.

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