The gold standard, most agent-friendly UI for email-based support. Integrates cleanly with Salesforce. Powerful triggers and automation available.
Weaker for website-chat based support. Time intensive to implement and integrate.
Sync your data to Salesforce and track your team as they move work forward. Set goals for timelines, response/cycle times, work in progress, and more. Any process, any object in Salesforce.
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If you're not sure where to start with a dysfunctional team, start with repetitive work. Figure out how things are supposed to work, and where they aren't happening this way.