
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
Let $a$ and $b$ be real numbers such that
\[ a^3 - 3a^2 - 4a + 12 = 0 \quad \text{and} \quad 3b^3 + 9b^2 - 11b - 3 = 0. \]
Compute $a + b.$

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