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

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