The development of large language models (LLMs) capable of following instructions and engaging in conversational interactions sparked increased interest in their utilization across various support tools. We investigate the utility of modern LLMs in assisting professional writers via an empirical user study (n=30). The design of our collaborative writing interface is grounded in the cognitive process model of writing that views writing as a goal-oriented thinking process encompassing non-linear cognitive activities: planning, translating, and reviewing. Participants are asked to submit a post-completion survey to provide feedback on the potential and pitfalls of LLMs as writing collaborators. Upon analyzing the writer-LLM interactions, we find that while writers seek LLM's help across all three types of cognitive activities, they find LLMs more helpful in translation and reviewing. Our findings from analyzing both the interactions and the survey responses highlight future research directions in creative writing assistance using LLMs.