Deployment with custom Github Actions workflow for jekyll site - deployment

Question

I've tried to deploy a Jekyll blog site with my custom Github Actions workflow file. Build and deployment have succeeded so far.
But every time I push the sources to this git repository, the GitHub Pages bot action is executed as well. So two workflow files are executed after pushing.
I've switched the 'Build and Deployment' setting from 'deploy from branch' to 'Github Actions'. After I've done it, my custom GitHub Actions are executed only. But the changes have not been deployed to my github.io blog site.
My question is do I have to use the GitHub Pages bot action, if not,
Is there any solution to my workflow file?
name: build site with jekyll and deploy on github pages
on:
push:
branches:
- master
jobs:
jekyll:
runs-on: ubuntu-20.04
steps:
# checkout code
- uses: actions/checkout#v2
# Use ruby/setup-ruby to shorten build times
# https://github.com/ruby/setup-ruby
- uses: ruby/setup-ruby#v1
with:
ruby-version: 3.1 # Not needed with a .ruby-version file
bundler-cache: true # runs 'bundle install' and caches installed gems automatically
# use jekyll-action-ts to build
# https://github.com/limjh16/jekyll-action-ts
- uses: limjh16/jekyll-action-ts#v2
with:
enable_cache: true
# use actions-gh-pages to deploy
# https://github.com/peaceiris/actions-gh-pages
- name: Deploy
uses: peaceiris/actions-gh-pages#v3
with:
# GITHUB_TOKEN secret is set up automatically
github_token: ${{ secrets.GITHUB_TOKEN }}
publish_dir: ./_site