Everard's assignment - Todor must be found innocent. Any other route is sub-optimal because it results in him being expended as an agent.
Meet Lenox Pierce - you must gather all of the evidence and figure out what caused Patrick's death; in general this means questioning everyone you can, examining all of the data on the terminal in the SGS mortuary, getting information about Patrick from Jon the Beautiful, and getting information on the Spectres from Oskar. Also as of the last patch it's a valid solution to kill the suspect after confronting him with the evidence, rather than having to identify the murder weapon etc with Lenox.
Meet Ohad Xander - get information from Jon, acquire a Hercules sample, have Pasquale analyse it, and then either give the data to Gene or upload it to the Trim network yourself using the terminal in the under-passages where all of the Motioners hang out.
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It's almost always Everard's assignment that people mess up.