Step 1: Recall the NO signaling pathway. Endothelial NO is a gas that crosses easily into nearby smooth muscle cells.
Step 2: Inside the cell, NO stimulates soluble guanylate cyclase to convert GTP into cyclic GMP, raising intracellular cGMP levels.
Step 3: Elevated cGMP behaves as a second messenger like cAMP, switching on protein kinases that relax the muscle and dilate the vessel.
Step 4: The other choices, the BRCA genes and interleukins, belong to DNA repair and immune signaling and have nothing to do with NO. Hence NO acts by increasing cGMP.
\[\boxed{\text{cGMP}}\]