
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 $f(x) = a^{x-1}$ for $x \geq 0$, where $a > 0$ and $a \neq 1$.
(1) If the graph of $f(x)$ passes through the point $(2, \frac{1}{2})$, find the value of $a$.
(2) Determine the range of the function $y = f(x)$ for $x \geq 0$.

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