
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 venusian prophet Zabruberson sent to his pupils a  $ 10000$ -letter word, each letter being  $ A$  or  $ E$ : the *Zabrubic word*. Their pupils consider then that for  $ 1 \leq k \leq 10000$ , each word comprised of  $ k$  consecutive letters of the Zabrubic word is a *prophetic word* of length  $ k$ . It is known that there are at most  $ 7$  prophetic words of lenght  $ 3$ . Find the maximum number of prophetic words of length  $ 10$ .

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