How to allow immediate user input after one parallel node completes in LangGraph?

[bedead]

I'm building a multi-agent system with LangGraph where:

chatbotAgent handles user inputs and responds quickly.
otherAgent runs in parallel to process background tasks (like writing data to another state attribute).
I'm using graph.astream(..., stream_mode="values") which allows me to stream the chatbot response immediately.

❗The problem:
Even after chatbotAgent returns its result, I can’t send the next user input until otherAgent also completes. The entire graph run blocks further interaction.

✅ What I want:
To let the user continue chatting with chatbotAgent without waiting for other parallel nodes (like otherAgent) to finish.