Using OpenMP with GPU - recursion

Question

Everyone good time of day!
I would like to ask the advice of the respected community about the use of GPU computing power instead of or together with the CPU.
I have a well-functioning program based on recursive search of all kinds of combinations of some events, paralleled using OpenMP to run on all available processor cores.
The pseudocode C++ is as follows:
// #includes
// function announcements
// declaring a global variable:
QVector<QVector<QVector<float>>> variant; // (or "std::vector")
int main() {
// reads data from file
// data are converted and analyzed
// the variant variable containing the current best result is filled in (here - by pre-analysis)
#pragma omp parallel shared(variant)
#pragma omp master
// occurs call a recursive algorithm of search all variants:
PEREBOR(Tabl_1, a, i_a, ..., reс_depth);
return 0;
}
void PEREBOR(QVector<QVector<uint8_t>> Tabl_1, QVector<A_struct> a, uint8_t i_a, ..., uint8_t reс_depth)
{
// looking for the boundaries of the first cycle for some reasons
for (int i = quantity; i < another_quantity; i++) {
// the Tabl_1 is processed and modified to determine the number of steps in the subsequent for cycle
for (int k = 0; k < the_quantity_just_found; k++) {
if the recursion depth is not 1, we go down further: {
// add descent to the next recursion level to the call stack:
#pragma omp task
PEREBOR(Tabl_1_COPY, a, i_a, ..., reс_depth-1);
}
else (if we went down to the lowest level): {
if (condition fulfilled) // condition check - READ variant variable
variant = it_is_equal_to_that_,_to_that...;
else
continue;
}
}
}
}
Unfortunately, I don't have a CPU with a thousand cores at my disposal, and without this, the algorithm works for a very long time. At the place where I work, I was advised to think about using a GPU to speed up calculations. I learned that OpenMP can work with video cards (and especially with NVidia), but OpenACC also does it well.
In this regard, my main question is whether it is possible to simply and, at the same time, effectively set the execution of a recursive algorithm on a GPU? Can this give a noticeable acceleration relative to the CPU? If so, maybe OpenACC will do better? And is it possible to give instructions to the video card through the "#pragma omp task", or are other instructions REQUIRED? And how would it be possible to combine calculations on the CPU and GPU?
Thank you so much for any help!
P.S. I apologize for my English, which is not my native language :)