该问题的解决方法是在CodeBuild项目中添加"npm run build"或"yarn run build"命令，并将自定义动作的框架定义为"CODE_BUILD"。建议使用以下代码作为参考：

import * as codebuild from '@aws-cdk/aws-codebuild';

const sourceOutput = new codepipeline.Artifact();

const codeBuildProject = new codebuild.PipelineProject(this, 'BuildProject', {
  buildSpec: codebuild.BuildSpec.fromObject({
    version: '0.2',
    phases: {
      install: {
        commands: [
          'npm install'
        ],
      },
      build: {
        commands: [
          'npm run build' // modify this command
        ],
      }
    },
    artifacts: {
      files: [
        '**/*'
      ],
      "base-directory": 'dist'
    },
  }),
});

const customAction = new codepipeline_actions.CodeBuildAction({
  actionName: 'Build',
  project: codeBuildProject,
  input: sourceOutput,
  outputs: [websiteBuild],
});

pipeline.addStage({
  stageName: 'Build',
  actions: [customAction],
});

其中，"npm run build"可以根据项目使用的构建工具和脚本进行修改。