In Settlers of Catan, multiple action can be taken per turn, so you may want to go back and undo an action after you think about it more. I am wondering whether actions can be undone after proceeding on to something else. Such as building a road, building a settlement then, after realizing the road shouldn't be built, removing it. So, my question is, can action be undone after moving on?
All building is simultaneous within a build action
Here is what the Catan rulebook has to say on the subject of building.
Now you can build. Through building, you can increase your victory points, expand your road network, improve your resource production, and/or buy useful development cards. To build, you must pay specific combinations of resource cards (see the Building Costs Card). Take the appropriate number of roads, settlements, and/or cities from your supply and place them on the game board. Keep development cards hidden in your hand.
This implies that all the building is chosen and paid for all at once.
However, that is not to say you can roll back your entire turn.
Combined Trade/Build Phase
The separation of the trade and build phases was introduced to make the sequence easier to learn for beginners. We recommend experienced players ignore this separation.
After rolling for resource production, you can trade and build in any order (you can trade, build, trade again and build again, etc.). You can even use a harbor on the same turn you build a settlement there. Using this method speeds up the game a lot.
This means that there is separation between builds done before and after trade actions. You cannot build a city, trade with another player, and then roll back the decision to build that city and use the new cards to instead build something else. Those were separate actions.
And arguably, this means that it's allowable to take two separate build actions in a row. After all, you could take a trade action and not do any trading, which gives you two consecutive build actions. Which is useful, because building a development card reveals new information to you, and might change how you want to do the rest of your building.
How much 'undoing' is allowed will depend on your play group.
Ultimately, it's up to your play group to decide what constitutes formally 'taking' an action. Does declaring that you're building a city count as taking the action? Placing the city on the map? Depositing the resource cards?
This doesn't have to be a formal decision the group makes. Many groups are informal about this process, and frequently allow a decision to be reversed as long as it is easy to do so, no other players have made decisions in the meantime, and no new information (like looking at a newly build development card) has been revealed. However, rewinding and adjusting a turn takes time and energy on the part of all involved, and if invoked frequently can quickly get wearing. Groups who have members who have a tendency to waffle on their decisions are far more likely to require clear decision points after which decisions cannot be undone. Additionally, tournament play tends to require clear decision points, as action rewinds can be used to deliberately confuse and frustrate the opponents by interrupting and changing their planning.