Any property owner may accept the assessment of damages in his favor made by the board, or acquiesce in their failure to assess damages in his favor, and shall be construed to have done so unless he gives to the board, within thirty (30) days after the assessment is filed, notice in writing that he demands an assessment of his damages by a jury. In that event, the board shall institute an action to condemn the lands that must be taken or damaged in the making of the improvement, which action shall be in accordance with the proceedings provided in § 14-117-305.