
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
Positive numbers $a, b, c$ satisfy the equation $a^{2}b + b^{2}c + c^{2}a = 3$. Find the minimum value of the expression

$$
A = a^{7}b + b^{7}c + c^{7}a + ab^{3} + bc^{3} + ca^{3}
$$

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