Create a rugged vector illustration of a lumberjack wielding an axe, celebrating the hardworking spirit of American labor. The lumberjack should be depicted in a full-body pose, wearing a plaid shirt and sturdy pants, with a raised axe that conveys strength and determination. Surround him with circular sawblades and tree silhouettes to enhance the theme of labor and nature. Use an earthy color palette of browns, forest greens, and deep reds to create a rustic vibe. The design should feature bold outlines (4-6 points) for clarity and visual impact. The background should be transparent or white, allowing the elements to stand out prominently. Ensure the illustration is created at a high resolution (300 DPI) for print quality. Incorporate textured details in the lumberjack's clothing and the axe to add depth and realism. Consider adding a woodgrain texture to the background to enhance the rustic feel and connect the illustration to the lumberjack's environment. Incorporate subtle gradients in the colors to create depth and dimension, particularly in the lumberjack's clothing and the surrounding elements.