As you know, vacuuming is beneficial for cleaning the laminate floors. Similarly, if you notice some tough stains, such as the oily and dirty ones, they are harder to remove and require deep cleaning.
It would be best to use a mop or a broom for deep cleaning. What you need to do here is to have a tub of warm or lukewarm water and soak the broom or mop in the warm water.
Then mop the floor using it to clean the surface, making sure you don’t mop extra to cause the floor any damage. After mopping, use a soft cloth to wipe it over the laminate floor to dry out the water.
Make sure to use a soft microfiber cloth as the harsh cloth will damage the floor and make the surface rough.