
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
The language of the mumbo-jumbo tribe consists of $k$ different words. The words are composed of only two types of letters, $A$ and $O$. No word can be transformed into another word by removing some letters from the end. What is the minimum number of letters that the complete vocabulary of the language contains?

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