
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 inhabitants of the island of Alphabeton use the Trundic script, consisting of $15$ letters, A through O. Each word in their language is $5$ letters or less. To be considered a valid word, each word must contain the letter A and the letter B at least once. How many words are possible?

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