
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 following problem was used for Vietnamese team selection test 1996. I have a solution, but it is quite complicated. 

Find the minimal value of function
f(a, b, c) = (a+b)^4 + (b+c)^4 + (c+a)^4 - (4/7)(a^4+b^4+c^4), where a, b, c run over reals.

*Vietnamese Team selection 1996 problem **

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