
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
For a positive integer $n \geq 2$, consider the complex numbers $\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}$ such that $\left|\alpha_{i}\right| \leq 1$ for $i = 1, 2, \ldots, n$. Find the minimum possible value of $\sum_{i=1}^{n} \left| 1 + \alpha_{i} \right| + \left| 1 + \prod_{i=1}^{n} \alpha_{i} \right|$.

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