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Add LiteLLM activity sample #1363

Job	Run time
build-lint-test (3.10, windows-latest)	8m 17s
build-lint-test (3.10, macos-arm)	8m 18s
build-lint-test (3.10, ubuntu-latest)	7m 4s
build-lint-test (3.10, macos-intel)	11m 8s
build-lint-test (3.14, macos-arm)	7m 21s
build-lint-test (3.14, windows-latest)	8m 9s
build-lint-test (3.14, ubuntu-latest)	7m 0s
build-lint-test (3.14, macos-intel)	12m 42s
	1h 9m 59s