
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
In a shop on Taobao, a specialty product from Xiaogan is sold. According to past experience, disregarding other factors, the daily sales volume $y$ (in kilograms) of this product and the selling price $x$ (in yuan per kilogram, $1 < x \leqslant 5$) satisfy the following: when $1 < x \leqslant 3$, $y = a(x - 3)^2 + \frac{b}{x - 1}$ ($a$ and $b$ are constants); when $3 < x \leqslant 5$, $y = -70x + 490$. It is known that when the selling price is 2 yuan per kilogram, 600 kilograms of this product can be sold daily; when the selling price is 3 yuan per kilogram, 150 kilograms of this product can be sold daily.
(1) Find the values of $a$ and $b$, and determine the function expression of $y$ with respect to $x$;
(2) If the sales cost of this product is 1 yuan per kilogram, determine the value of the selling price $x$ (accurate to 0.1 yuan per kilogram) that maximizes the shop's daily profit $f(x)$ from selling this product.

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