
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 $f(x)=a^x$ $(a > 0, a \neq 1)$ passing through the point $(2,9)$.

(1) Find the analytical expression of function $f(x)$ and its range.

(2) If the equation $(f(x))^2 - 2f(x) + k = 0$ has exactly two distinct real roots, find the range of the real number $k$.

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