Among the cases reported in the ward with Edward Burke as the alderman and happened in the community area with the highest population, provide the report number of the crime with the highest beat.
the highest population refers to max(population); report number refers to report_no; the highest beat refers to max(beat)
SELECT T2.report_no FROM Ward AS T1 INNER JOIN Crime AS T2 ON T2.ward_no = T1.ward_no INNER JOIN Community_Area AS T3 ON T3.community_area_no = T2.community_area_no WHERE T1.alderman_first_name = 'Edward' AND T1.alderman_last_name = 'Burke' ORDER BY T2.beat DESC, T3.population DESC LIMIT 1