Every deal has a Tasks tab in its right-hand sidebar — every open task or approval from any automator running on that deal, whoever it's assigned to (not just yours). It's the same row you'd see on My Tasks, just scoped to this one deal, and without the deal-address column since you're already looking at it.
Claim, complete, and verify the same way you would anywhere else — see Completing tasks and approvals. With nothing open, the tab reads No open tasks on this deal — since tasks come from a running automator, an Open Automators button takes you straight to that tab to start one.