GAC and Trust Agreement

[KMG77]

If a plan is wholly invested in a Group Annuity Contract would it be inconsistent to also have a Trust Agreement in place? Without the Trust Agreement (or trust provisions) the duties, powers, liability, etc. of the Trustees are not set forth.

The Trustees are both named and Trustees by virtue of being the contract holder.

While I've been able to find references to plans that both had a GAC and a Trust Agreement, I wasn't able to determine if there were either "true" trust assets in addition to the GAC or if the contributions hit a trust before the GAC or like in my situation the Trust Agreement would primarily outline Trustee provisions.

Thoughts?