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My apple trees all spawned on islands not connected to my starting location, so I needed to canoe across to find them.

You can technically have the tool-using ones keep their inventory with a log in it.

Fill their inventory with Stone except for the last slot, in which you put a Log, and their hand, in which you put the tool.

With this, if they burn their Log, they will stow their tool, grab a log, and then cycle back to their tool, leaving them back with a full inventory and a tool in hand.  Then they'll do their task up until their hands are empty (and their tool broke), after which they'll go back to the tool storage to grab a fresh tool.

You can add an empty "Until (X) storage is not full" just after the "until Inventory Full" block if you want them to not bother doing their task if your storage is full for that item anyway.  For example, I could say "Repeat Until Clay Storage is not full : (Nothing)" and the bot will just sit there waiting for there to be room in Clay Storage before they start digging again. Since waiting around like this doesn't use any fuel, it's okay that the program will wait there until there's room in storage.

When the bug is fixed that is making the bots consume their entire inventory, you don't have to prime them with stone anymore.  They'll still have a full inventory of logs they won't be using, of course, but the time saved not having to hand them a bunch of stones first makes up for it.

Edit: Actually, there's some problems with this, because for some reason, burning a log that's at the front of your inventory won't actually shuffle the rest of the inventory down.  Instead, it leaves the gap at the front of the inventory, meaning it messes up the cycling since when you store the item, it'll be at the beginning instead of at the end.  So you have to use a full inventory of logs, and use Cycle item Up instead of down.

Where are you trying to craft an axe?

If you're at the start of the game, pick up a Stick so that you're holding it in your hand, and then left click on a Stone on the ground and it will pop up with the option to craft a Crude Axe or a Crude Shovel.

If you're a little later, you need a Basic Workbench to craft a Wooden Axe, which will require one Pole and one Plank, which you can get by using an axe on a plank or a log respectively, or at a saw.

Nesting "Repeat X times" won't work properly, since they actually only have a single variable for the number of times a loop has repeated. So unfortunately this cannot be done at present.

It will either need to be changed to allow multiple "X times" nesting, or changed to prevent you from nesting them in the first place.