Final answer:
The social worker should refer the family for assessment and treatment due to the serious nature of the adolescent's behavior changes, which include engaging in illegal activities, risk-taking, and declining academic performance.
Step-by-step explanation:
The situation described presents a 13-year-old boy's drastic change in behavior, manifesting in declining grades, arrest for shoplifting, setting small fires, and a distinct shift in appearance. Such psychosocial changes are indicative of turmoil that goes beyond what might be considered average adolescent rebellion, and these could suggest underlying issues that require professional intervention. Therefore, the social worker should refer the family for assessment and treatment. This action is recommended because the behaviors the adolescent is exhibiting—engaging in unlawful activities, increased risk-taking, and significant decline in academic performance—are concerning and could be symptoms of a deeper issue. An assessment can help identify if there are mental health issues, trauma, or environmental stressors contributing to this behavior, while treatment can provide needed support and coping strategies.