Find user on multiple condition after aggregation result

I want to find user who have user_action searched-for-cake and got-cake.

sample index is as follow.

{
{
user_id:"ad97b3fe-0d55-4133-9367-1",
user_action:"searched-for-cake"
},

{
	user_id:"ad97b3fe-0d55-4133-9367-1",
	action:"got-cake"		
},

{
	user_id:"ad97b3fe-0d55-4133-9367-3",
	action:"need-help"		
},

{
	user_id:"ad97b3fe-0d55-4133-9367-4",
	user_action:"searched-for-cake"		
},

{
	user_id:"ad97b3fe-0d55-4133-9367-4",
	action:"got-cake"		
},

{
	user_id:"ad97b3fe-0d55-4133-9367-3",
	action:"got-cake"		
}

}

Take a look at the nested datatype, the nested query and also the nested aggregation

hope this helps!