
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 freight truck travels at a constant speed of $x$ kilometers per hour for a distance of $130$ kilometers $\left(50\leqslant x\leqslant 100\right)$ (unit: kilometers per hour). Assuming the price of gasoline is $2$ yuan per liter, and the truck consumes $\left(2+\dfrac{x^{2}}{360}\right)$ liters of fuel per hour, and the driver's wage is $14$ yuan per hour.

(1) Find the expression of the total cost $y$ of this trip in terms of $x$.

(2) Determine the value of $x$ that minimizes the total cost of this trip, and find the minimum cost.

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