In this scenario, are you allowed to begin the overtaking manoeuvre of the preceding vehicle while exercising extreme caution?

In the photo you are driving on a two-way road through a forest behind a grey car; on the right there is a yellow triangular sign A-1 "dangerous bend to the right", and the road is about to turn. Even if you exercise particular caution, you are not allowed to begin overtaking. The answer is: no.

The Road Traffic Act prohibits overtaking a power-driven vehicle on a bend marked with warning signs; the exception on a two-way roadway applies only to a section with marked lanes and to driving without entering the part of the roadway for the opposite direction where road markings prohibit this. Sign A-1 tells you that you are approaching a dangerous bend, and overtaking started now would already take place on the bend, in the lane for the opposite direction, without a view of what is beyond the curve. The centre line here is broken, but this does not open the way to overtaking: just before the bend it changes into a double solid line, and a car coming from the opposite direction is already visible; there is only one lane in your direction, so any overtaking means driving in the lane for oncoming traffic. Particular caution does not cancel the ban; you follow the grey car through the bend and overtake only on a straight section with good visibility.

Legal basis: Art. 24 para. 7 point 2, para. 8 point 2 and para. 1 point 1 of the Road Traffic Act (Prawo o ruchu drogowym); § 4 para. 1 of the Regulation on road signs and signals