
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
Three girls \( A, B \) and \( C \), and nine boys are to be lined up in a row. Let \( n \) be the number of ways this can be done if \( B \) must lie between \( A \) and \( C \), and \( A \) and \( B \) must be separated by exactly 4 boys. Determine \( \lfloor n / 7! \rfloor \).

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