
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 that the fuel consumption per hour of a certain airplane is proportional to the cube of its speed, and when the airplane flies at a speed of \( a \) km/h, the fuel cost is \( m \) yuan (assuming the price of fuel is constant). Additionally, suppose that for every hour of flight, apart from the fuel cost, other costs amount to \( n \) yuan. Determine the most economical speed for the airplane to fly \( p \) kilometers and the total cost.

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