
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
Consider the set $M = \{4, 3, -1, 0, 1\}$. Let $M_1, M_2, \ldots, M_{31}$ be all the non-empty subsets of M. For each subset $M_i$ ($i = 1, 2, \ldots, 31$), let $m_i$ be the product of all elements in $M_i$. Calculate the sum $m_1 + m_2 + \ldots + m_{31}$.

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