
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
A certain tourist attraction was opened in an area, with approximately 1 million visitors in the first year and about 1.2 million visitors in the second year. A mathematics interest group predicted by synthesizing various factors that: ① The number of tourists visiting this attraction will increase year by year; ② The number of tourists will not reach 1.3 million in any year. The interest group wishes to find a function $y=f(x)$ to fit the relationship between the $x$-th year ($x \geq 1$) since the attraction opened and the number of visitors $y$ (in ten thousand) of that year.
(1) According to the above predictions, please describe the properties of the function $y=f(x)$ in mathematical language;
(2) If $f(x) = \frac{m}{x} + n$, try to determine the values of $m$ and $n$, and examine if this function conforms to the above predictions;
(3) If $f(x) = ab^x + c$ ($b > 0$, $b \neq 1$), to make this function comply with the above predictions, try to determine the range of values for $b$.

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