Lacking something fundamental with Compose

I am trying to convert a view based screen to Compose and while what I need should be very basic, somehow I can't get this to work. The use case at hand is a serial task where one step follows the other and the UI should reflect progress. But I seem to miss something fundamental because none of my Text() will update. Below is a simplified example of what I got:

    override fun onCreate(savedInstanceState: Bundle?) {
        …
        
        setContent {
            Import()
        }
    }
    
    
    @Composable
    fun Import() {        
        var step1 by remember { mutableStateOf("") }
        var step2 by remember { mutableStateOf("") }
          
        Column() {
                Text(text = step1)
                Text(text = step2)
            }
        }

        step1 = "Open ZIP file"
        val zipIn: ZipInputStream = openZIPFile()
        step1 = "✓ $step1"
    
        step2 = "Extract files"
        val count = extractFiles()
        step2 = "✓ $step2"
        …
    }

If I set the initial text in the remember line, like this

var step1 by remember { mutableStateOf("Open ZIP file") }

the text will show, but also never gets updated.

I also tried to move the logic part into a separate function which gets executed right after setContent() but then the step1/step2 aren't available for me to update.

#######

Edit:

Well, as expected this turned out to be really easy. I have to break this one

var step1 by remember { mutableStateOf("Open ZIP file") }

into 2 statements:

var step1String =  mutableStateOf("Open ZIP file")

With step1String as a class wide variable so I can change it from other functions. In the Import() composable function al I need is this:

var step1 by remember { step1String }

Have to say Compose is growing on me… :-)