
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 \(f(x)=3^{2-x}-1\) and \(g(x)=x^2-ae^x\), if they are "first-degree zero-point functions" of each other, determine the range of the real number \(a\).

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