
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 domain of the function $f(x)$ is $R$, and $f(x)=x^3f(\frac{1}{x})$ for $x∈(-∞,0)∪(0,+∞)$, and $f(x)+f(y)-2xy=f(x+y)$, find the value of $f(4)$.

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