
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 \( a, b, c > 0 \), find the maximum value of the expression

\[ A = \frac{a^3(b+c) + b^3(c+a) + c^3(a+b)}{(a+b+c)^4 - 79(abc)^{4/3}}. \]

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