If it is an order, directed to a single person, an alternative could be:
rem proximam fac
But I'm not quite convinced.
The problem with deinde is that it is an adverb, and as such, it needs to modify a verb. To modify rem (a noun) you need an adjective. Proxima means both nearest and next (in feminine). I like this ambiguity in the careless context you want to give to the sentence. Proxima has been translated as next, e.g. in (Cic. Tul. 9):
Proxima nocte, iam fere cum lux adpropinquaret... The next night, when it was near day-break...
An alternative for next is Sequens. It also means the next at least in a sequence in time. Disclosure: I'm not sure either is the best adjective for next, but are fit ones anyway. I think proxima is better.
Facite is plural, as in the order directed to two or more people. Proximam rem facite or facite rem proximam are valid. (Word order in Latin is pretty free: the -m in rem means that's the thing being done; putting the object before the verb adds emphasis on the former).
If it is more like "let's do the next thing" you could say rem proximam faciamus. You have to choose one verbal form. Unfortunately Latin does not offer that exquisite ambiguity English has, that allows to convey so many meanings at a time.
Another verb for to do in this context could be ago, hence age/agite sequentem rem or rem sequentem age/agite. They are different and which one to use could depend on what kind of thing is to be done. There is not an exact mapping with English verbs to do and to make.
Now, I'm not sure how idiomatic it is in Latin to apply the verb facio (as in fac, or even ago) to a thing (as in rem). But if you want to reproduce the vagueness of do the thing, I can't think of a better option.
If your Latin motto can be more precise in order to be idiomatic, to complete a task/perform a duty is well said with the verb conficio.
It is also common to replace [adjective] + thing, by the sole adjective in its neuter gender form: bonum-good thing, mala-bad things, etc. Generalizing this rule you could say proximum-next/nearest thing. I'm not sure this is fully idiomatic either, but sounds good to me. So depending on the addressee, you have these three alternatives:
proximum confice (you, one person)
proximum conficite (you, two or more people)
proximum conficiamus (we)
The first one (proximum confice) could arguably be read with ambiguity, since proximum could also be the subject (it would make a very weird sentence though, so I wouldn't worry about that).
A bunch of additional ideas:
Alternative (though more specific) words for thing: Duty might be pensum. Some words for task that come to my mind are: opus (n., meaning work as in work of art), or the related opera (f.) and operatio (f.), negotium (n., occupation), and even labor (although it's more closely related to suffering).
Looking at the sense you want to give, perhaps something in the line of let's go to work can do the trick too.