
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 an alphabet of  $n$  letters, is  $syllable$  is any ordered pair of two (not necessarily distinct) letters. Some syllables are considered  $indecent$ . A  $word$  is any sequence, finite or infinite, of letters, that does not contain indecent syllables. Find the least possible number of  indecent syllables for which infinite words do not exist.

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