You bought it because you had ideas. Every one of those ideas was formed from the outside, with none of the context that explains why the business is the shape it is. The first ninety days are for acquiring that context.
Days 1–30: read everything
Every support ticket for six months. The single highest-value activity available to you. You'll learn the product, the customers and the real problems in one pass.
Every cancellation reason. Read them in order. Patterns appear by the fortieth.
The last two years of revenue, by customer. Find out who actually pays for this.
All existing documentation, and note what's missing — that's your first writing task.
Days 31–60: fix the boring things
Now do the work that has no downside — the maintenance the previous owner deferred because it wasn't interesting:
Set up monitoring, if there isn't any. You should learn about downtime before your customers do.
Fix the failed-payment flow. It's usually neglected and it's usually the cheapest revenue in the business.
Update the dependencies that are dangerously behind.
Test the backup restore. Again. Properly.
Answer support faster than the previous owner did. Customers notice, and it costs nothing.
Days 61–90: make one change
One. Chosen from what you learned in the first sixty days, not from what you assumed on day zero. Measure it properly, in isolation. If it works, then make the next one.
What kills acquisitions in the first quarter
A redesign. Existing users didn't ask for it, and it breaks the muscle memory they pay for.
A price rise, too early. Sometimes right eventually. Never right in month one, before you understand who's price-sensitive.
Killing the "pointless" feature. It is always load-bearing for the customer segment you haven't met yet.
Going quiet on support. The fastest way to convert a stable base into churn.
Changing the positioning. The customers you have found you through the old message.
The business already works. Your job in the first quarter is to not break it while you find out why it works — and that discovery is worth more than any of the ideas you arrived with.