
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 positive integers \(a\), \(b\), and \(c\) that are pairwise coprime, and satisfy:
$$
a^{2} \mid (b^{3} + c^{3}), \quad b^{2} \mid (a^{3} + c^{3}), \quad c^{2} \mid (a^{3} + b^{3}),
$$
find the values of \(a\), \(b\), and \(c\).

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