
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

Solve the following system of equations in positive integers:

$$
\left\{\begin{aligned}
a^{3}-b^{3}-c^{3} & =3 a b c \\
a^{2} & =2(b+c)
\end{aligned}\right.
$$

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