
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
The set \( M = \{-1, 0, 1, -2, 2, 10, 20, -30, 99, -100\} \) has 10 elements. Let all non-empty subsets of \( M \) be denoted \( M_i \), \( i = 1, 2, 3, \ldots, 1023 \). The product of all elements in each \( M_i \) is denoted as \( m_i \) (\( i = 1, 2, 3, \ldots, 1023 \)). Find \( \sum_{i=1}^{1023} m_i \).

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