How to properly use of Synergy in a sentence?

Synergy is not the word to use in the way you want it in your sentence. The word to use is multitask. Synergy would refer more to people working together to produce a far more greater result.

Synergy Usage

Synergism, in general, may be defined as two or more agents working together to produce a result not obtainable by any of the agents independently. The word synergy or synergism comes from two Greek words: erg meaning "to work", and syn meaning "together"; hence, synergism is a "working together."

A cost synergy refers to the opportunity of a combined corporate entity to reduce or eliminate expenses associated with running a business. Cost synergies are realized by eliminating positions that are viewed as duplicate within the merged entity.

I think "Multitask" is the word you are looking for.

Human multi-tasking or multitasking is the performance by an individual of appearing to handle more than one task at the same time. The term is derived from computer multitasking. An example of multitasking is listening to a radio interview while typing an email....

My application of "third-wave" business process management drives synergies amongst the diverse organizational units of the new knowledge-driven economy; it utilizes cross-unit expertise at the corporate level that combines to strengthen value chains and build greater competitive advantages and exciting growth opportunities, moving forward.