
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
This is a 12-point problem.

A delivery truck travels uniformly at a speed of $x$ kilometers per hour for 130 kilometers ($50 \leq x \leq 100$, unit: kilometers/hour). Assume the price of gasoline is 2 yuan per liter, and the truck consumes $\left(2+\frac{1}{x}\right)$ liters of gasoline per hour. The driver's wage is 14 yuan per hour.

(1) Find the expression for the total cost $y$ of the trip as a function of $x$.
(2) At what value of $x$ to minimize the total cost of the trip, and find the minimum cost.

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