Is it possible to display the install actions in a list in Inno Setup?

Is it possible to list the progress like it does in other installers?

You can monitor changes in WizardForm.StatusLabel and WizardForm.FilenameLabel and add them to your custom list box progress view.

const
  GWL_WNDPROC = -4;
  SB_VERT = 1;
  SB_BOTTOM = 7;
  WM_VSCROLL = $0115;
  WM_ERASEBKGND = $0014;

type
  WPARAM = UINT_PTR;
  LPARAM = LongInt;
  LRESULT = LongInt;

var
  OldStatusLabelWndProc: LongInt;
  OldFilenameLabelWndProc: LongInt;
  OldProgressListBoxWndProc: LongInt;
  ProgressListBox: TNewListBox;
  PrevStatus: string;
  PrevFileName: string;

function CallWindowProc(
  lpPrevWndFunc: LongInt; hWnd: HWND; Msg: UINT; wParam: WPARAM;
  lParam: LPARAM): LRESULT; external 'CallWindowProcW@user32.dll stdcall';  
function SetWindowLong(hWnd: HWND; nIndex: Integer; dwNewLong: LongInt): LongInt;
  external 'SetWindowLongW@user32.dll stdcall';

procedure AddProgress(S: string);
begin
  if S <> '' then
  begin
    ProgressListBox.Items.Add(S);
    ProgressListBox.ItemIndex := ProgressListBox.Items.Count;
    SendMessage(ProgressListBox.Handle, WM_VSCROLL, SB_BOTTOM, 0);
  end;
end;

function StatusLabelWndProc(
  hwnd: HWND; uMsg: UINT; wParam: WPARAM; lParam: LPARAM): LRESULT;
begin
  Result := CallWindowProc(OldStatusLabelWndProc, hwnd, uMsg, wParam, lParam);
  if PrevStatus <> WizardForm.StatusLabel.Caption then
  begin
    AddProgress(WizardForm.StatusLabel.Caption);
    PrevStatus := WizardForm.StatusLabel.Caption;
  end;
end;

function FilenameLabelWndProc(
  hwnd: HWND; uMsg: UINT; wParam: WPARAM; lParam: LPARAM): LRESULT;
begin
  Result := CallWindowProc(OldFilenameLabelWndProc, hwnd, uMsg, wParam, lParam);
  if PrevFileName <> WizardForm.FilenameLabel.Caption then
  begin
    AddProgress(WizardForm.FilenameLabel.Caption);
    PrevFileName := WizardForm.FilenameLabel.Caption;
  end;
end;

function ProgressListBoxWndProc(
  hwnd: HWND; uMsg: UINT; wParam: WPARAM; lParam: LPARAM): LRESULT;
begin
  // reduce flicker
  if uMsg = WM_ERASEBKGND then
  begin
    Result := 1;
  end
    else
  begin
    Result :=
      CallWindowProc(OldProgressListBoxWndProc, hwnd, uMsg, wParam, lParam);
  end;
end;

procedure InitializeWizard();
begin
  OldStatusLabelWndProc :=
    SetWindowLong(WizardForm.StatusLabel.Handle, GWL_WNDPROC,
      CreateCallback(@StatusLabelWndProc));
  OldFilenameLabelWndProc :=
    SetWindowLong(WizardForm.FilenameLabel.Handle, GWL_WNDPROC,
      CreateCallback(@FilenameLabelWndProc));

  WizardForm.ProgressGauge.Top := WizardForm.FilenameLabel.Top;

  ProgressListBox := TNewListBox.Create(WizardForm);
  ProgressListBox.Parent := WizardForm.ProgressGauge.Parent;
  ProgressListBox.Top :=
    WizardForm.ProgressGauge.Top + WizardForm.ProgressGauge.Height + ScaleY(8);
  ProgressListBox.Width := WizardForm.FilenameLabel.Width;
  ProgressListBox.Height :=
    ProgressListBox.Parent.ClientHeight - ProgressListBox.Top - ScaleY(16);
  ProgressListBox.Anchors := [akLeft, akTop, akRight, akBottom];
  OldProgressListBoxWndProc :=
    SetWindowLong(ProgressListBox.Handle, GWL_WNDPROC,
      CreateCallback(@ProgressListBoxWndProc));
  // Lame way to shrink width of labels to client width of the list box,
  // so that particularly when the file paths in FilenameLabel are shortened
  // to fit to the label, they actually fit even to the list box.
  WizardForm.StatusLabel.Width := WizardForm.StatusLabel.Width - ScaleY(24);
  WizardForm.FilenameLabel.Width := WizardForm.FilenameLabel.Width - ScaleY(24);
end;

procedure DeinitializeSetup();
begin
  // In case you are using VCL styles or similar, this needs to be done before
  // you unload the style.
  SetWindowLong(
    WizardForm.StatusLabel.Handle, GWL_WNDPROC, OldStatusLabelWndProc);
  SetWindowLong(
    WizardForm.FilenameLabel.Handle, GWL_WNDPROC, OldFilenameLabelWndProc);
  SetWindowLong(
    ProgressListBox.Handle, GWL_WNDPROC, OldProgressListBoxWndProc);
end;