
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
Bob writes a random string of 5 letters, where each letter is either \( A \), \( B \), \( C \), or \( D \). The letter in each position is independently chosen, and each of the letters \( A \), \( B \), \( C \), \( D \) is chosen with equal probability. Given that there are at least two \( A \)'s in the string, find the probability that there are at least three \( A \)'s in the string.

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