The action is definitely broken or worn. When the hammer is cocked the cylinder should lock solidly with no movement.
The gun is absolutely NOT to be fired in this condition.
You have the very first model, the Model 1889. Again, this was the very first double action, swing-out cylinder revolver ever made.
The Colt Model 1889 New Navy revolver had NO cylinder locking notches on the outer perimeter of the cylinder like more modern guns. The cylinder locks on the REAR of the cylinder.
"706" is a factory assembly number. These numbers were stamped on major parts during finishing and fitting to insure the parts stayed together. The serial number was stamped later, and it's stamped on the bottom of the butt in these early models.
The actual serial number is 7960, which means the gun was made in 1890, the second year of production.
The numbers that year ran from 5200 to 10399.
Since there are no US Navy marks, this was a commercial model.
The key identifying features of the 1889 are:
The cylinder with long flutes, no outer locking notches, and the cylinder locking on the ejector ratchet at the rear.
Serial number under 31,000.
The patent dates of August 5, 1884, November 6, 1888.
Two or three digit assembly numbers on cylinder release, the crane, the frame inside facing the crane, the bottom of the barrel breech, the cylinder, and inside the grips. Note again, these are NOT the serial number).