
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
In the Cartesian coordinate plane $(xOy)$, the curve $y=2x^{2}+ \frac{a}{x}$ ($a$ is a constant) passes through point $P(-1,-30)$. What is the sum of the maximum and minimum values of the function $y=2x^{2}+ \frac{a}{x}$ in the interval $[1,4]$?

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