
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
Six boys and \( a \) girls are randomly arranged in a line. Each boy is adjacent to at least one other boy, and the probability that at least four boys stand together is \( p \). If \( p \leq \frac{1}{100} \), find the minimum value of \( a \).

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