Cooling nozzle vanes of a turbine engine

An assembly for a turbine engine, comprising:

• an engine structure including a plenum, a reverse flow combustor, a nozzle structure, a cooling circuit, a turbine wall and an intermediate structure;
• the reverse flow combustor disposed in the plenum and comprising a combustion chamber;
• the nozzle structure arranged at an outlet from the combustion chamber, the nozzle structure including a first platform, a second platform and a plurality of vanes arranged circumferentially about an axis, the first platform forming a first boundary of a flowpath through the nozzle structure, the second platform forming a second boundary of the flowpath, and the plurality of vanes extending across the flowpath from the first platform to the second platform;
• the cooling circuit extending in the first platform and between a circuit inlet into the cooling circuit and a circuit outlet from the cooling circuit, the circuit inlet fluidly coupled with and disposed along the plenum, and the circuit outlet fluidly coupled with and disposed along the flowpath;
• the turbine wall axially overlapping the reverse flow combustor and the nozzle structure;
• the intermediate structure extending along the flowpath between a downstream end of the first platform and an upstream end of the turbine wall;
• and
• the circuit inlet disposed along a portion of the plenum bordered by the first platform and the intermediate structure.