A multi-digit number is called optimistic if its digits increase from left to right. If the digits of the number decrease from left to right, we say that it is a pessimistic number. Find all optimistic numbers for which the following is true:

$\triangleright$ the arithmetic mean of the digits of the given number is 7,

$\triangleright$ if we swap the first digit with the last digit in this number, we get a pessimistic number.
If by swapping the first and last digit an optimistic number turns into a pessimistic number, it is evident that such a number can have at most three digits.

a) two-digit numbers: Only two pairs of numbers $(5,9)$ and $(6,8)$ satisfy the condition that their arithmetic mean is 7. From this, we get that the sought optimistic numbers are 59 and 68.

b) three-digit numbers: For the arithmetic mean of the three digits to be 7, their sum must be 21. We find all suitable decompositions of the number 21. They are the triples $(9,8,4),(9,7,5)$ and $(8,7,6)$. From this, we get that the sought optimistic numbers are: 59, 68, 489, 579, and 678.

[for justification that only two-digit and three-digit numbers are considered - 1 point, for each correct number - 1 point]