
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