A hospital developed a design process consisting of the following steps: Plan, Design, Measure, Assess, and Improve. Below is a list of $21$ specific activities that comprise these five steps in random order. Place the activities in the most appropriate order within the correct step of the design process.

$1.$ Implement design.

$2.$ Identify out of control conditions.

$3.$ Establish design team.

$4.$ Identify and validate customer requirements.

$5.$ Develop business plan.

$6.$ Propose new concept.

$7.$ Submit proposal.

$8.$ Create design to meet requirement.

$9.$ Identify and evaluate best practices.

$10.$ Analyze causes.

$11.$ Identify causes of out$-$of$-$control conditions

$12.$ Define measures to assess design performance.

$13.$ Monitor process performance.

$14.$ Pilot or test design

$15.$ Monitor the new process design.

$16.$ Identify new improvement opportunities.

$17.$ Disseminate improvements throughout the organization.

$18.$ Identify potential solutions to reduce out of control conditions.

$19.$ Select the best solution to improve control.

$20.$ Implement the best solution to improve control.

$21.$ Verify proposal alignment with strategic objectives.