Evokimov M.A.

A gold prospector has a pile of gold sand weighing 37 kg (and he has no more sand), a two-pan balance, and two weights of 1 and 2 kg. The prospector can perform actions of two types:

- balance the scales, i.e., if the scales are currently not in equilibrium, he can pour some sand from one pan to the other so that the scales come into balance;
- add sand to balance, i.e., if the scales are currently not in equilibrium, he can add sand to one of the pans so that the scales come into balance.

Of course, he can only perform each of these actions if he has enough sand.

How can he, in two actions with the scales, get a pile that weighs exactly 26 kg? Mixing two piles of sand, as well as simply placing something on the scales, does not count as an action.
The first action the gold prospector can take is to place all the sand on the left pan of the scales, and both weights on the right - and then sift the sand until equilibrium is achieved. In the end, he will have $20$ kg of sand on the left and $17$ kg of sand (and two weights of $1+2$ kg) on the right. The second action should be to place the $20$ kg of sand on the left pan of the scales, and the $2$ kg weight on the right - and once again balance the scales until there is $11$ kg of sand on the left and $9$ kg of sand (and one weight of $2$ kg) on the right. Finally, the heap of $9$ kg obtained in the second action should be mixed with the remaining heap of $17$ kg from the first action.