
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 the language of wolves has two letters  $F$  and  $P$ , any finite sequence which forms a word.   А word  $Y$  is called 'subpart' of word  $X$  if Y is obtained from X by deleting some letters (for example,   the word   $FFPF$  has 8 'subpart's: F, P, FF, FP, PF, FFP, FPF, FFF).  Determine  $n$  such that  the  $n$  is the greatest number of 'subpart's can have n-letter word language of wolves.


F. Petrov,  V. Volkov

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