It depends on how important it is for you to follow the scheme you describe in your question. The key problem is that API Gateway doesn't let you use a colon : in your resource name.
If it is not important to follow the scheme
Consider making your API scheme more RESTful.
Perhaps instead of performing an analyzeEntities action on documents, consider that your requests to analyze the documents are themselves resources which can be created...
e.g:
POST /documents/analyzeRequest[s]
(where body describes the type of request)
or
POST /documents/analyzeEntitiesRequest[s]
These would allow you to add GETs later on to list previous/current requests
If it is important to follow the scheme
So, specifying a : in your resource path results in the error:
Resource's path part only allow a-zA-Z0-9._- and curly braces at the beginning and the end.
The workaround to this is to create a new resource and check the Configure as proxy resource box.
Creating a proxy resource allows you to defer routing decision making to a lambda function, for any path which matches the rule.
e.g. ANY /{proxy+} would match all requests.
Note: If you then added a separate resource GET /foo, your proxy resource would not handle GET /foo, since a more specific rule now exists.
So, with a proxy resource set up, you would need to write a lambda that invokes the appropriate lambda function, based on your routing rules.