It doesn’t matter if you were the sole person responsible for a task or if you worked with a group -- if you’re comfortable doing the task on your own, it’s okay to say “planned and executed events” instead of “assisted with the planning and execution of events.” You’re not lying by leaving out the fact that others were working alongside you. And if you’re not sure that a responsibility is something you can do on your own, take the opportunity to showcase your teamwork skills by using verbs like “collaborated.” Think hard about what you’re actually capable of, and use that as the basis for your resume bullet points.
Keep in mind that if you’re looking for a position where you’ll be supporting an individual or team, you should include "supported" and "assisted" somewhere on your resume, but they definitely should not appear more than once in each section. Even one bullet point that shows administrative support or a similar skill is enough to prove you can do a job that requires administrative assistance, and the rest of your bullet points can be used to highlight other important skills. And if you’re applying for anything higher than an assistant position, you can lose any assistant-related verbs entirely.
Remember, your resume is the first tool that will make an impression on a hiring manager, so you want to find every possible way to maximize its impact and stand out from the crowd. To do this, it’s important to take ownership of your responsibilities -- don’t undersell yourself because you’re feeling timid.