
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 \( p(x) \) be the real polynomial \( 1 + \alpha_1 x^{m_1} + \alpha_2 x^{m_2} + \ldots + \alpha_n x^{m_n} \), where \( 0 < m_1 < m_2 < \ldots < m_n \). For some real polynomial \( q(x) \) we have \( p(x) = (1 - x)^n q(x) \). Find \( q(1) \) in terms of \( m_1, \ldots, m_n \).

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