
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 \(a, b, c\) are such that \(a+b+c=3\). Find the minimum value of the expression

\[
A=\frac{a^{3}+b^{3}}{8ab+9-c^{2}}+\frac{b^{3}+c^{3}}{8bc+9-a^{2}}+\frac{c^{3}+a^{3}}{8ca+9-b^{2}}
\]

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