"supervising" in the noun sense
1. supervision, supervising, superintendence, oversight
management by overseeing the performance or operation of a person or group
"supervising" in the verb sense
1. oversee, supervise, superintend, manage
watch and direct
"Who is overseeing this project?"
2. monitor, supervise
keep tabs on keep an eye on keep under surveillance
"we are monitoring the air quality"
"the police monitor the suspect's moves"
Source: WordNet® (An amazing lexical database of English)
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