
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 \( F \) be the collection of all sequences of the form \( \left(A_{1}, A_{2}, \cdots, A_{n}\right) \), where each \( A_{i} \) is a subset of \( B = \{1, 2, \cdots, 10\} \). Let \( |A| \) represent the number of elements in set \( A \). Then \( \sum_{F}\left|\bigcup_{i=1}^{n} A_{i}\right| = \) ?

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