
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 alphabet contains \( n > 1 \) letters; a word is any finite sequence of letters in which any two neighboring letters are different. A word is called good if it is not possible to delete all letters except for four such that the remaining sequence is of the form \( a a b b \), where \( a \) and \( b \) are different letters. Find the maximum possible number of letters in a good word.

(D. Khramiov)

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