
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 cargo truck travels at a constant speed of $x$ km/h over a distance of 130 km, with traffic regulations limiting the speed to $50 \leqslant x \leqslant 100$ (units: km/h). Assume the price of gasoline is 2 yuan/L, the truck consumes $\left(2 + \frac{x^2}{360}\right)$ L of gasoline per hour, and the driver's wage is 14 yuan/h.

(1) Find an 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 the lowest? Find the minimum cost.

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