chromeos: Remove the last IME methods from ash::SystemTrayDelegate

ash/system/ime_menu/ime_menu_tray.cc

Index: ash/system/ime_menu/ime_menu_tray.cc
diff --git a/ash/system/ime_menu/ime_menu_tray.cc b/ash/system/ime_menu/ime_menu_tray.cc
index 8ce578885796987f81bd2424eed756ff7c3bc811..bd845fac4c1a5e2a31fa5d0a1af64520421c88b8 100644
--- a/ash/system/ime_menu/ime_menu_tray.cc
+++ b/ash/system/ime_menu/ime_menu_tray.cc
@@ -13,10 +13,10 @@
 #include "ash/shell.h"
 #include "ash/shell_port.h"
 #include "ash/strings/grit/ash_strings.h"
+#include "ash/system/ime/ime_util.h"
 #include "ash/system/ime_menu/ime_list_view.h"
 #include "ash/system/tray/system_menu_button.h"
 #include "ash/system/tray/system_tray_controller.h"
-#include "ash/system/tray/system_tray_delegate.h"
 #include "ash/system/tray/system_tray_notifier.h"
 #include "ash/system/tray/tray_constants.h"
 #include "ash/system/tray/tray_container.h"
@@ -445,11 +445,8 @@ bool ImeMenuTray::PerformAction(const ui::Event& event) {
 void ImeMenuTray::OnIMERefresh() {
   UpdateTrayLabel();
   if (bubble_ && ime_list_view_) {
-    SystemTrayDelegate* delegate = Shell::Get()->system_tray_delegate();
-    IMEInfoList list;
-    delegate->GetAvailableIMEList(&list);
-    IMEPropertyInfoList property_list;
-    delegate->GetCurrentIMEProperties(&property_list);
+    IMEInfoList list = ime_util::GetAvailableIMEList();
+    IMEPropertyInfoList property_list = ime_util::GetCurrentIMEProperties();
     ime_list_view_->Update(list, property_list, false,
                            ImeListView::SHOW_SINGLE_IME);
   }
@@ -536,7 +533,7 @@ void ImeMenuTray::OnKeyboardSuppressionChanged(bool suppressed) {
 }
 
 void ImeMenuTray::UpdateTrayLabel() {
-  Shell::Get()->system_tray_delegate()->GetCurrentIME(&current_ime_);
+  current_ime_ = ime_util::GetCurrentIME();
 
   // Updates the tray label based on the current input method.
   if (current_ime_.third_party)