
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
The cost of flying a plane for 1 hour consists of two parts: a fixed part of 4900 yuan, and a variable part P (yuan) which is a function of the plane's flying speed v (kilometers per hour) given by the formula $P=0.01v^2$. Given that the distance between locations A and B is a (kilometers).
(1) Please write the total cost $y$ (yuan) of flying the plane from location A to location B as a function of the speed $v$ (kilometers per hour);
(2) At what speed does the plane incur the minimum cost?

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