Which process in the carbon cycle is primarily responsible for converting atmospheric $\mathrm{CO_2}$ into organic molecules in plants?

Write the chemical equation for photosynthesis: The general equation for photosynthesis is $6\mathrm{CO_2} + 6\mathrm{H_2O} \xrightarrow{\text{light energy}} \mathrm{C_6H_{12}O_6} + 6\mathrm{O_2}$. This shows how $\mathrm{CO_2}$ is transformed into organic molecules.

Compare photosynthesis with other processes: Decomposition breaks down organic matter into simpler compounds, releasing $\mathrm{CO_2}$. Combustion burns organic matter, releasing $\mathrm{CO_2}$. Respiration converts organic molecules back into $\mathrm{CO_2}$ during energy production. None of these processes convert $\mathrm{CO_2}$ into organic molecules like photosynthesis does.