
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 a function $f(x)=a^{x-1}$ where $a>0$ and $a \neq 1$, the graph passes through the point $(3, \frac{1}{9})$.
(1) Find the value of $a$;
(2) Determine the range of the function $f(x)=a^{2x}-a^{x-2}+8$ when $x \in [-2, 1]$.

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