input: Write a function to create and manage an environment object that can execute and analyze Python code. The environment includes predefined global variables and the ability to add additional global variables. It can execute Python code, analyze it for variable usage and imports, and capture and display output from executed code. If the environment fails to parse the code, it should log the error traceback and provide analysis results if possible.
  
  Add a test case to assert the creation of the environment object and the execution and analysis of a sample Python code. If the code executes successfully, the function should return the analysis results and the output captured from the executed code. If the code fails to execute, the function should return the error traceback logged during execution.
  
  assert analyze_and_execute('.', 'print("Hello, World!")') == True
  assert analyze_and_execute('invalid_path', 'print(1 / 0)') == False
output: def analyze_and_execute(path, code):
      try:
          exec(code, globals())
          return True
      except Exception as e:
          return False