Add an "hint" to my first simple python number guessing game

Question

I tried to make my first game on python. There's something I don't understand because when I try enter "hint" has an answer, I get this error code:

---

Traceback (most recent call last):  
  File "C:/Users/Lenovo/PycharmProjects/Test/while loop test.py", line 18, in <module>  
    if int(answer) == secret_number:  
ValueError: invalid literal for int() with base 10: 'hint'

---

Can you give me any idea what i've done wrong? I tried to reassign the type string to the variable "answer" but it doesn't work.
Here's the code:

# Guessing game
import random
# Game explanation
print("Welcome to the Guessing game ! \nYou have 3 chances to find the number between 1 and 10, otherwise it ends!")

# Game variables
secret_number = random.randint(1, 11)
random_hint_number = random.randint(1, 5)
secret_number_hint = ("The secret number is between ", (secret_number - random_hint_number), (secret_number + random_hint_number))
guess_count = 0
guess_limit = 3

# game engine
while guess_count < guess_limit:
    answer = input("What is your guess?")
    guess_count += 1
    if int(answer) == secret_number:
        print("You won!")
        break
    elif answer == "hint":
        print(f"{secret_number_hint}")
        guess_count -= 1
    elif int(answer) != secret_number:
        print("Wrong answer")
        print("If you need an hint, type in: hint")
print("Sorry you failed")

Answer 1

You'll need to test the input in the proper order

if answer == "hint":
    print(f"{secret_number_hint}")
    guess_count -= 1
    continue 

if int(answer) == secret_number:
    print("You won!")
    break
else:
    print("Wrong answer")
    print("If you need an hint, type in: hint")