When we say that someone "reaches into" something, we typically mean that they are extending their hand or arm into a particular area or item. Some synonyms for this phrase might include "dips into," "delves into," "dives into," or "plunges into." These words all suggest a sense of exploration or investigation, implying that the person in question is investigating or searching for something within what they are reaching into. Other possible synonyms might include "extends into," "reaches within," "penetrates," or "probes," depending on the exact context and the connotations you want to convey. Ultimately, the choice of synonym will depend on the specific circumstances of the situation at hand.