we appreciate all reviewers for their correct summarisation of our contributions as (1) Introduce the ice-start problem

We thank all the reviewers for their time to provide comments and the positive feedback from reviewer 1 and 4. Also, In the following, we will address the questions proposed by each reviewer. This demonstrates the broad applicability of the proposed method. For AUIC, we used its full name in line 205. However, we would like to highlight our novel inference method for BELGAM. We will add a detailed introduction of this encoder in the appendix of the revised version.