
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
It is known that for real numbers \(a\) and \(b\), the following equalities hold:

\[ 
a^3 - 3ab^2 = 11, \quad b^3 - 3a^2b = 2 
\]

What values can the expression \(a^2 + b^2\) take?

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