
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
If you don't drink, you can drive; if you drive, you can't drink. If a person drinks and wants to hire a designated driver from a place 45 km away to help them return, assuming the speed limit on the local road is 50 km/h. The price of gasoline is 8 yuan per liter. When the car is traveling at a speed of x km/h, the fuel consumption rate is $({3+\frac{{{x^2}}}{{360}}})$ L/h. It is known that the designated driver charges 56 yuan per hour. Determine the most economical speed for this trip to minimize the total cost and find the minimum cost.

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