The URL '/reports/123/' is pointing to a 'report' resource and it should not matter what backend operations will be acted on it.
When thinking about resource-url and its associated operations, the only relevant operations are "GET/PUT/POST/DELETE"
Then map the business operations (like generate PFD report) to the url+HTTP-Op+params.
Like in this case, map 'generate PDF report" to "GET /reports/123/"
use-case-1: simple get report
GET /reports/123/
return: {pdf-report}
use-case-2: customized report
GET /reports/123/
param: {"json info passed along with the get operation"
return: {pdf-report}
The the backend can detect if there are input from the client to decide what specific backend operations should be taken to generate the report.
Hope this help!