Makefile with multiple libraries

Comment faire un Makefile qui inclut d'autre librairies, qui doivent-elles aussi etre "Make".
Voici mon Makefile (temporaire) pour push_swap dans lequel je compile 2 fichiers (main.c et parsing.) avec ma Libft et mon ft_printf. Bien sur, le Makefile ne relink pas.

Pour plus de contexte, voici mon dossier push_swap:
./push_swap:
drwxr-xr-x 4 phautena 2024_paris   71 Jun 26 12:37 ft_printf
drwxr-xr-x 2 phautena 2024_paris 4.0K Jun 26 12:37 Libft
-rw-r--r-- 1 phautena 2024_paris 1.5K Jun 26 12:37 Makefile
-rwxr-xr-x 1 phautena 2024_paris  23K Jun 26 12:37 push_swap
-rw-r--r-- 1 phautena 2024_paris 1.1K Jun 26 12:18 push_swap.h
-rw-r--r-- 1 phautena 2024_paris 1.2K Jun 26 12:22 main.c
-rw-r--r-- 1 phautena 2024_paris 1.8K Jun 26 12:19 parsing.c

# **************************************************************************** #
#                                                                              #
#                                                         :::      ::::::::    #
#    Makefile                                           :+:      :+:    :+:    #
#                                                     +:+ +:+         +:+      #
#    By: phautena <[email protected]>          +#+  +:+       +#+         #
#                                                 +#+#+#+#+#+   +#+            #
#    Created: 2024/06/26 12:24:27 by phautena          #+#    #+#              #
#    Updated: 2024/06/26 12:37:13 by phautena         ###   ########.fr        #
#                                                                              #
# **************************************************************************** #

NAME = push_swap

SRC = main.c parsing.c

CC = cc -Wall -Werror -Wextra -ggdb

OBJ = ${SRC:.c=.o}

LIBFT_ARCHIVE = ./Libft/libft.a

PRINTF_ARCHIVE = ./ft_printf/libftprintf.a

.c.o:
    ${CC} -c $< -o $@

all: ${NAME}

${NAME}: ${LIBFT_ARCHIVE} ${PRINTF_ARCHIVE} ${OBJ}
    ${CC} ${OBJ} ${LIBFT_ARCHIVE} ${PRINTF_ARCHIVE} -o ${NAME}

${LIBFT_ARCHIVE}:
    make -sC ./Libft

${PRINTF_ARCHIVE}:
    make -sC ./ft_printf

clean:
    make clean -sC ./Libft
    make clean -sC ./ft_printf
    rm -f ${OBJ}

fclean: clean
    make fclean -sC ./Libft
    make fclean -sC ./ft_printf
    rm -f ${NAME}

re: fclean all

.PHONY: all clean fclean re