ValleyCare Health System, which operates two hospitals and other sites in Pleasanton and Livermore, is exploring a merger with Stanford Hospital & Clinics, the two parties said Thursday afternoon. ValleyCare has had financial difficulties recently, and former CEO Marcy Feit left the organization abruptly in early February. Officials at both organizations say ValleyCare and Stanford have signed a non-binding letter of intent to affiliate. Such a move could bolster ValleyCare, which could use the support of a larger, wealthier system, and Stanford Hospital, which has been engaged in a vigorous competition with academic medical center rival UCSF Medical Center in recent years to grab more doctors, patients and philanthropic support throughout the Bay Area. Some are calling that rivalry the "clash of the titans."