
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
In a language $,$  an alphabet with  $25$  letters is used $;$  words are exactly all sequences of  $($  not necessarily different  $)$  letters of length  $17.$  Two ends of a paper strip are glued so that the strip forms a ring $;$  the strip bears a sequence of  $5^{18}$  letters $.$  Say that a word is singular if one can cut a piece bearing exactly that word from the strip $,$  but one cannot cut out two such non-overlapping pieces $.$  It is known that one can cut out  $5^{16}$  non-overlapping pieces each containing the same word $.$  Determine the largest possible number of singular words $.$  
*(Bogdanov I.)*

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