
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 the real numbers $\alpha$, and $\beta$ which satisfy the equations $\alpha^{3}-3 \alpha^{2}+5 \alpha=1$ and $\beta^{3}-3 \beta^{2}+5 \beta=5$, find the value of $\alpha + \beta$.

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