
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
Given real numbers \(\alpha\) and \(\beta\) satisfying:
\[
\alpha^{3} - 3 \alpha^{2} + 5 \alpha = 1, \quad \beta^{3} - 3 \beta^{2} + 5 \beta = 5,
\]
find \(\alpha + \beta\).

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