Try |View::HandleAccessibleAction| before falling back to fixed actions.

chrome/browser/ui/aura/accessibility/automation_manager_aura.cc

Index: chrome/browser/ui/aura/accessibility/automation_manager_aura.cc
diff --git a/chrome/browser/ui/aura/accessibility/automation_manager_aura.cc b/chrome/browser/ui/aura/accessibility/automation_manager_aura.cc
index 11f50f0fc4980439abd235909769fa85d0c78be3..ad9122d0f8c7d6b6fe76dc0c83db5212087809a7 100644
--- a/chrome/browser/ui/aura/accessibility/automation_manager_aura.cc
+++ b/chrome/browser/ui/aura/accessibility/automation_manager_aura.cc
@@ -85,6 +85,12 @@ void AutomationManagerAura::PerformAction(
     const ui::AXActionData& data) {
   CHECK(enabled_);
 
+  if (current_tree_->HandleAccessibleAction(data)) {
+    // This accessible action is handled by custom action implemented by the
+    // target view.
+    return;
+  }
+
   switch (data.action) {
     case ui::AX_ACTION_DO_DEFAULT:
       current_tree_->DoDefault(data.target_node_id);