return $false on a sync step with powershell

Dear community.

I am trying to synchronize the status of the groups of AD in ServiceNow.

ServiceNow has a field called active that can be true or false (Boolean). As the groups in AD don't have this field, I am checking if the group is in a certain OU and returning true or false accordingly.

However, I get an error "String was not recognized as a valid Boolean."

This is the code

$GroupName = $srcObj["name"];
$Logfile = "C:\Temp\DebugStatus.txt"
[bool] $active
Connect-QADService -proxy

$dN = (Get-QADGroup -identity $GroupName ).DirectoryEntry.distinguishedName
if ($dN -like '*,OU=Deprovisioned Groups,*')
{
  $active=$false
  $message = $active.gettype().fullname
  Add-Content $Logfile $message
  $message = $GroupName + $active
  Add-Content $Logfile $message
}
else
{
  $active=$true
  $message = $active.gettype().fullname
  Add-Content $Logfile $message
  $message = $GroupName + $active
  Add-Content $Logfile $message
}
return $active;

I have tried passing directly $false, $true, 0, 1 .... 

In the log file that I create for the checking of the script I get this (which is type, group name and content of the boolean variable)

System.Boolean
Test deprovisioned group False

Can you tell me how should I specify to get it done?

Best regards