Ordering async tasks

OrderedTasks.swift

// Built with Swift 6 (Xcode 16b1)
actor Accumulator {
    static let shared = Accumulator()

    var values: [String] = []

    // A couple of approaches, neither of which works.
    func add(value: String) { values.append(value) }

    nonisolated func addSync(value: String) { Task { await add(value: value) } }
}

final class C: Sendable {
    func run() {
        // Neither of these approaches seem to work, though both together do, so it's a race condition.
        Accumulator.shared.addSync(value: "sync")
//        Task { await Accumulator.shared.add(value: "async") }
    }
}

C().run()

// How can I ensure that `values` is updated before `values` returns without making `run` async?
// I'm not asking for `run` to block until it's done. I'm asking for this `await` to block until
// the previous operation completes.
print(await Accumulator.shared.values) // This return []
print(await Accumulator.shared.values) // This returns ["sync"]