Another possibility is that she starts some new hobbies. Annabeth could take up drawing, for example. She can use this new form of expression to convey her feelings about missing Percy. Or she might join a sports team at school. Physical activity can be a great distraction. Through these new experiences, she might also discover new aspects of herself.
She might focus on her studies more. Since Annabeth is really into knowledge, she could pour all her energy into her schoolwork, like spending extra hours in the library or on research projects.
Well, Annabeth is a strong character. She may start by grieving privately, not wanting to let her vulnerability show. As she is pregnant, she would feel an even greater sense of responsibility. She could start documenting stories about Percy for the baby, so that the child can know who their father was. And she would probably try to find a new purpose in life, centered around raising the baby in a way that Percy would have wanted.
Percy might be a source of comfort for Annabeth. School can be a tough place sometimes, with all the academic pressure and social drama. Percy is someone she can always rely on, and without him, she feels less secure. Maybe he has a unique way of making her laugh or feel better when she's down, and she misses that a great deal.
Percy might initially feel a great deal of anger. He's been wronged by those he thought were his friends. But then, with Annabeth by his side, he could start to focus on finding out the truth. He might use his skills, like his combat abilities and strategic thinking, to figure out who or what is behind the betrayal.
Their relationship might develop through more in - depth conversations. Since they are engaged, they start talking about their future, like where they want to live. Maybe Percy wants to live near the ocean and Annabeth has other ideas, and they have to compromise.
On the other hand, she could try to honor Percy's sacrifice. Annabeth might focus on the reasons why Percy died for her and strive to fulfill any tasks or goals that he might have hoped she would achieve. She would carry on his legacy in a positive way, even though she is heartbroken.
Annabeth could also try to solve the problem that's making Percy cry. If it's related to a quest or a danger, she'll start thinking of ways to fix it. In some fanfictions, she might say 'Don't worry, we'll figure this out together.' and then start making a plan.
Annabeth could also be angry, not at Percy but at the situation or the forces that led to his death. She might vow revenge and start on a journey to find out who or what was responsible for Percy's sacrifice and make them pay. This could lead her into a whole new set of adventures and challenges as she tries to come to terms with her loss.
She might be heartbroken at first. She could try to jog Percy's memory by showing him things that were important to them.
Over time, Percy would likely start to have a glimmer of hope. He might meet someone who gives him a lead or has a bit of information about a possible way to revive Annabeth. This hope would give him the strength to keep going, even when things seem impossible. He'd focus all his energy on this one goal, shutting out other distractions in his life.
It can develop through this moment of closeness. Just the act of her sleeping on him can show a level of trust, which Percy might recognize and it deepens their bond.