The Mishna Brura in Hilchos Tisha B’Av brings a powerful hint as to what we should be doing on a fast day.
Bringing the Posuk in Yona, when Yona went to Ninveh to tell them to do Teshuva.
The posuk explains that the people of Ninveh fasted and donned garments made of sackcloth, and we are told that “HaShem saw their actions”.
The Mishna Brura explains “their actions” to be “teshuva” – ie. not fasting and sackcloth. These did not sway the balance in their favour enough to save their lives, it was however their Teshuva that caused HaShem to spare them.
So too, when we are obligated by the Rabbis to fast, this is a smaller factor of the day, for we are only fasting to inspire us to do Teshuva and bring HaShem to our hearts – this is the real work for us to be doing on a fast day!
