Okay, the user wants to play a number-guessing game. Let me make sure I understand the rules correctly.

First, I need to pick a random number between 1 and 10 and keep it fixed throughout the game. Then, I ask the user to guess the number. They'll respond with their guess, and if they get it right, I congratulate them and end the game. If not, we keep going until they guess correctly.

Wait, I should check if the user's instructions are clear. The rules state that I choose the number first, then they guess one number at a time. Each incorrect guess leads to another attempt. Since the number is fixed, I can't change it once selected.

I need to generate a random number now. Let me use a random number generator between 1 and 10. Let's say I pick 7. Now, I should prompt the user to make their first guess. They might say any number. If they guess 7, I need to congratulate them. If not, I tell them to try again.

Wait, but how do I handle the user's input? Since I'm simulating this, I need to wait for their response each time. Oh, right, in this setup, the user will provide their guesses step by step. So each time they input a number, I check against my chosen number.

Let me structure the response correctly. First, I'll announce that I've chosen a number and ask for their guess. Then, depending on their input, I'll either congratulate them or ask again.

Wait, but in the initial message, the user hasn't guessed yet. So my first message should be the prompt for their first guess. Let me make sure I don't reveal the number. Also, I need to remember the number throughout the interaction. Since this is a single conversation, I'll have to keep track of the chosen number across the exchanges.

Testing scenarios: If the user guesses correctly on the first try, respond with congratulations. If they guess wrong, say it's incorrect and ask again. Repeat until correct.

I should also make sure that the numbers are between 1 and 10. If the user inputs something outside that range, should I mention it? The rules say the user can only answer one number at a time, but it doesn't specify handling invalid inputs. Maybe I should assume they follow the rules and only input numbers 1-10. If they don't, perhaps I can inform them, but the original rules don't mention that. Hmm.

But according to the rules provided by the user, maybe I just proceed regardless. If they input a non-number or out-of-range, I might need to handle it, but the problem statement says they reply with a number each time. So maybe I can assume valid inputs.

So, in summary, the steps are:

1. Choose a random number (e.g., 7).

2. Ask user for their guess.

3. Check if their guess matches.

4. If yes, congratulate and end.

5. If no, repeat from step 2.

Now, implementing this in the chat. Since the user hasn't provided a guess yet, my first message should be prompting them to guess. Let me start with that.