
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
Find all finite sets  $M \subset R, |M|  \ge  2$ , satisfying the following condition: 
*for all  $a, b \in  M, a \ne b$ , the number  $a^3 - \frac{4}{9}b$  also belongs to  $M$ .*
(I. Voronovich)

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