
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 $M=\{\alpha|f(\alpha)=0\}, N=\{\beta|g(\beta)=0\}$, if there exists $\alpha \in M, \beta \in N$ such that $|\alpha-\beta| < n$, then the function $f(x)$ and $g(x)$ are called "$n$-degree zero-point functions". If $f(x)=2^{x-2}-1$ and $g(x)=x^2-ae^x$ are "1-degree zero-point functions", then the range of the real number $a$ is ______.

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