
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 logistics company's cargo truck travels a distance of 130 kilometers at a constant speed of $x$ kilometers per hour, where $40 \leqslant x \leqslant 100$ (unit: kilometers per hour). Assume that the price of gasoline is 6 yuan per liter, and the truck consumes $(2+ \frac{x^2}{360})$ liters of gasoline per hour. The driver's wage is 18 yuan per hour.

(1) Find the expression for the total cost $y$ of the trip in terms of $x$;

(2) For what value of $x$ is the total cost of the trip minimized, and find the minimum cost.

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