```
def run_thermostat(start: int, low: int, high: int, power: int, drifts: list) -> dict:
    for bound in (start, low, high):
        if isinstance(bound, bool) or not isinstance(bound, int):
            raise ValueError("temperatures must be integers")
    if low >= high:
        raise ValueError("low must lie strictly below high")
    if isinstance(power, bool) or not isinstance(power, int) or power <= 0:
        raise ValueError("power must be a positive integer")
    if not isinstance(drifts, list):
        raise ValueError("drifts must be a list")
    
    temp = start
    heated = 0
    switches = 0
    coldest = start
    
    for drift in drifts:
        if not isinstance(drift, int):
            raise ValueError("all elements of drifts must be integers")
        
        if temp < low and temp == coldest:
            coldest += power
        
        if heated == 1 and temp <= high:
            temp -= power
            switches += 1
        
        elif temp > high:
            heated = 0
            switches += 1
        
        temp += drift
    
    return {"temp": temp, "heated": heated, "switches": switches, "coldest": coldest}
```