The phrase "as I set about" is correct and usable in written English.
It can be used to indicate the beginning of an action or task that someone is undertaking.
Example: "As I set about organizing the event, I realized I needed more volunteers to help."
Alternatives: "as I began" or "as I started".
Early starts and late finishes ensued, as I set about restructuring the company.
"Bacon makes everything better," says the chef soothingly, as I set about making French toast to go with it.
Dancing to Schubert's lieder is a constant battle to balance this situation as I set about performing the material.
This allowed me to evaluate and recruit new talent as I set about rebuilding the Norfolk Prison Debating Society in 2011.
This was both a benefit and a complicating factor as I set about strategizing publicity for A Clockwork Orange, which was set to have its world premiere in New York on December 19,1971.
I set about gathering as much information as I have on the enquiries, including any data and any conclusions I may have already drawn, and set it out in an e-mail.
As punishment, I set about trying to forget him: the sound of his laughter, his height relative to mine, the content of the conversations we'd had after the lights went out but before we fell asleep.
As a result, I set about creating a holistic and integrative lifestyle plan that incorporated what I saw as essential Recovery-Centric elements for optimal wellness: mind (mental, spiritual), mouth (nutrition), and muscle (physical activity).
Barbara tells me I can meet with other band members the following day up at Can't Stop on E 55th street, so as the photographing develops I set about the Herculean task of trying to find the lift entrance.
The blueberries were, as promised, everywhere, and I set about the meditative work of crouching and plucking the tiny berries off the branches, one by one, until my hand was streaked with reddish-purple blueberry blood and I had gathered enough in my bag for a small pie.
As she put it: 'I set about keeping my resolve because I will not quarrel with myself, & because I shall give Wm pleasure by it when he comes home again.' Wilson quotes Ernest de Selincourt's description of Dorothy as 'probably the most remarkable and the most distinguished of English prose writers who never wrote a line for the general public'.
