How did Finch and Reese know that Hersh is going to poison Shaw

Question

In Person of Interest Season 2 Episode 16 "Relevance", Hersh grabs Shaw from behind and injects her with poison and she collapses. Later, Carter and Fusco tell the officer on the scene that it was an overdose and tell him to get some coffee. The officer leaves and they tell Leon, posing as an EMT, to haul the body away.

Later, Shaw wakes up in and ambulance and finds Reese and Finch and says that they showed up late. For which Finch points out that they wanted her to be believed as dead.

However, how do they know that Hersh is going to poison her when the goverment could have ordered her shot by someone else. Hersh is also shown to kill people by methods other than poison? He could have strangled or shot her.

Even for poison, how were they sure that they have enough time, Hersh might have given some quick poison.

Answer 1

To my knowledge they never explicitly state it in-universe. However in the scene with Reese and Shaw in the hotel room (following Root's interrogation of Shaw) establishes that the ISA (which Shaw worked for and Hersch still does) uses that particular poison as a method for subtle, quick executions. Combine that with Reese's experience in clandestine assassinations from his time working for the CIA would likely be enough for him to predict with reasonable confidence how they would try and eliminate Shaw and which poison they would use.