
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
Given the distance between places A and B is 120 km, according to traffic regulations, the speed limit for the highway between A and B should be constrained between 50 km/h and 100 km/h. Assuming the price of gasoline is 6 yuan per liter and the car's fuel consumption rate is $(3+\frac{x^2}{360}) L/h$, where $x$ is the speed of the car in km/h. The driver's wage is 42 yuan per hour. If we neglect other expenses, express the total cost of the trip, denoted as $y$ (in yuan), as a function of the car's speed $x$ (in km/h).  
(1) Express $y$ as a function of $x$;  
(2) What is the most economical speed and what is the minimum cost for this trip?

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