How to move a task from one package to another?

Hello,
I came across this doc:
https://developer.liquidplanner.com/docs/create-and-update-examples

However, I couldn't find the api which helps me in moving the task from one package to another. I see that parent_id needs to be updated, but I did not get any api which does that.

I also checked:
https://developer.liquidplanner.com/docs/moving-and-packaging-items

% curl https://app.liquidplanner.com/api/v1/workspaces/:id/tasks/:id/move_before?other_id=:id -X POST
% curl https://app.liquidplanner.com/api/v1/workspaces/:id/tasks/:id/move_after?other_id=:id -X POST

I know the workspace id and I know the task id(which needs to be moved). But where do I specify target package \ folder id in the above link?

I had a look at all the available APIs too. I did not find anything specific to parent_id updation:
https://app.liquidplanner.com/api/v1/help/urls

Kindly let me know.