
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
If the function $f(x)=(\frac{1}{2})^{-x^2+2x-2}$ is monotonically increasing on the open interval $D$, and for all $x\in D$, $2^{x^2-2ax+2a^2-1} > 1$, then the range of real number $a$ is ______.

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