
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
Find all positive integers \( n \) for which we can find one or more integers \( m_1, m_2, ..., m_k \), each at least 4, such that:
1. \( n = m_1 m_2 ... m_k \)
2. \( n = 2^M - 1 \), where \( M = \frac{(m_1 - 1)(m_2 - 1) ... (m_k - 1)}{2^k} \)

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