## 3 Results
### Coupling and Coordination Degrees Analysis  
Considering findings from previous studies [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25] and using the ArcGIS software and natural discontinuity classification method, the cities were divided into four categories based on their degree of coupling: barely coupled, primary coupling, intermediate coupling, and good coupling. They were also classified into five categories based on degree of coordination: barely coordinated, primary coordination, intermediate coordination, good coordination, and high-quality coordination. The degree of coordination refers to the degree of benign coupling during interaction. The degree of coupling refers to the degree of interaction between the two sides, regardless of the advantages and disadvantages. According to Figure 6, there was general consistency in the degrees of coupling and coordination of the LCCC system among Liaoning Province's  
Figure 4: Stacking histogram of LCCC subsystem. Huludao had the highest coupling degree. Yingkou and Tieling also had high-level coupling, with significant interdependence between subsystems. Across the entire province geological condition, and resource and environmental carrying capacities were higher in terms of coupling, while economic and social carrying capacities were lower. This was primarily because the geological environment restricted urban, economic, and social development to a certain extent, which in turn placed strain on resources and the environment. Second, the running-in stage was represented by the coupling degrees of Jinzhou City, Benxi City, and Fushun City. Shenyang, Dalian, Anshan, Dandong, and Liaoyang were  
Figure 5: Spatial distribution pattern of LCCC in Liaoning Province. Figure 6: Line chart of coupling and coordination degrees of LCCC system in Liaoning Province. cities with low-level coupling, indicating weak interactions between their subsystems. Liaoning Province's 14 prefecture-level cities generally had good coordination, with eight of them being above the intermediate coordination level (Table 5). The numerical coordination values of Shenyang, Dalian, and Benxi, which were all undergoing high-quality coordinated development, ranged from 0.8071 to 0.8228. Despite several issues such as growing population density, expanding construction land scales, and increasing population concentration in the cities, Shenyang and Dalian had good geological condition, rapid economic development, and substantial investments in public resources, infrastructure, and environmental protection. As a result, these regions can achieve high-quality coordinated development. Fuxin, Liaoyang, and Chaoyang had cooperative coordination levels between 0.7612 and 0.7740, indicating reluctant coordination. Although the ecological environments in these three prefecture-level cities were good, the overall coordination of the LCCC was subpar due to relatively unfavorable geological conditions, slow rates of economic development, and low degrees of infrastructure improvement. Each prefecture-level city in the Liaoning Province had similarly coupled and coordinated LCCC systems, and the benign interaction of subsystems demonstrated \"low in the west and high in the east\" spatial distribution (Figure 7). Figure 7 shows the gradient in coordination, from Chaoyang City and Fuxin City (in the west), which were at a reluctant coordination level, to the eastern part of the Liaoning Province, which contained regions of high-quality and good coordination in a semi-circular shape. To ensure the development of high-quality land space in Liaoning, the province had established two regional development coordination groups for the regions of Shenyang, Fushun, and Benxi,