How to run an async function properly that has any sync task that has a nested async task again

I want to run an async python script that has a sync part that has an assync task again

Is it possible?

This is an minimal example:

import asyncio
import threading

async def do_async3():
    # Asynchronous task logic
    print("Async Task 3 started")
    await asyncio.sleep(2)  # Simulating asynchronous work
    print("Async Task 3 completed")

def do1():
    print("Task 1")

def do2():
    print("Task 2")

def do4():
    print("Task 4")

def do5():
    print("Task 5")

async def main():
    print("main")
    # Synchronous tasks
    do1()
    do2()

    # Asynchronous task
    await do_async3()

    # Synchronous tasks after async task
    do4()
    do5()

# Call asyncio.run(main()) from a synchronous context
def run_main_sync(loop):
    print("run_main_sync")
    asyncio.set_event_loop(loop)
    loop.run_until_complete(main())

# New asynchronous function that calls run_main_sync
async def run_main_async():
    print("start")
    loop = asyncio.new_event_loop()
    asyncio.set_event_loop(loop)
    run_main_sync(loop)

# Run the asynchronous function
asyncio.run(run_main_async())

I want to execute the async task inside the do_async3 function get the result, do some sync tasks and wrap it in an other async task that is independent from the previous async task

But when I run the code I get the following:

(env) python proba.py
start
run_main_sync

Traceback (most recent call last): ... RuntimeError: Cannot run the event loop while another loop is running

sys:1: RuntimeWarning: coroutine 'main' was never awaited