
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 in natural numbers  $a,b,c$  the system \[\left\{ \begin{array}{l}a^3 -b^3  -c^3 = 3abc 
a^2 = 2(a+b+c)
 \end{array} \right.
\]

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