The ACLS algorithms for bradycardia and tachycardia essentially start the same way. In a nutshell, place the patient on a monitor, establish IV, apply oxygen. You can obtain a 12 lead ekg if you have time (if the patient is stable, but don’t delay therapy.)
The next box in the algorithm essentially defines stability. Does the patient have persistent chest pain likely casued by ischemia, is the patient hypotensive (typically a blood pressure less than 90 WITH SYMPTOMS, in other words, are there signs of shock, altered mental status, etc? Is the patient in acute heart failure?
Stability is different than "symptomatic." A patient who is generally stable may be symptomatic- orthostatic hypotension, mild shortness of breath, mild discomfort , palpitations. These are all signs that the patient may be symptomatic, (or feel the arrhythmia), but they are not overt signs of instability. For the symptomatic patient, it may be prudent to monitor, observe, and obtain expert consultation.
For the unstable patient, the prudent course of action is to act. Generally, the fastest course of action for the truly unstable patient is going to be electricity, either pacing, or cardioversion, depending on the algorithm. Drugs have their place as well, and can be effective. the point is not to delay definitive therapy in the unstable patient.