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Utilizing the Modified Hagedorn function with embedded flow, we analyze the transverse momenta (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula>) and transverse mass (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mi>T</mi></msub></semantics></math></inline-formula>) spectra of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>+</mo></msup></semantics></math></inline-formula> in Au–Au, Cu–Cu, and d–Au collisions at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt></semantics></math></inline-formula> = 200 GeV across various centrality bins. Our study reveals the centrality and system size dependence of key freezeout parameters, including kinetic freezeout temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>T</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>, transverse flow velocity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>β</mi><mi>T</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, entropy-related parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and kinetic freezeout volume (<i>V</i>). Specifically, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula> and <i>n</i> increase from central to peripheral collisions, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>T</mi></msub></semantics></math></inline-formula> and <i>V</i> show the opposite trend. These parameters also exhibit system size dependence; <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>T</mi></msub></semantics></math></inline-formula> are smaller in larger collision systems, whereas <i>V</i> is larger. Importantly, central collisions correspond to a stiffer Equation of State (EOS), characterized by larger <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>T</mi></msub></semantics></math></inline-formula> and smaller <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula>, while peripheral collisions indicate a softer EOS. These insights are crucial for understanding the properties of Quark–Gluon Plasma (QGP) and offer valuable constraints for Quantum Chromodynamics (QCD) models at high temperatures and densities.