Citation style varied by publication_types in Academic

I am using the Academic Theme. Could someone provide an example on how to customize citation by publication_types?

For example, I have publication_types = [3] for working papers, and publication_types = [2] for journal articles stored in ./content/publication/some_paper/

I want to make a small change to ./layouts/partial/li_citation.html file so that it will show different styles conditional on the publication_types. But I am not sure how to pass the publication_types variable to the html file.

For example, the default code first determines whether it is APA using the following code:
{{ if eq (site.Params.publications.citation_style | default "apa") "apa" }}

What I have in mind is to add something similar to the style detection, but conditional on the publication_types:
{{ if eq (publication_types | default "[2]") "[3]" }}
but I am not sure how publication_types is called in the html.