input: Write a function to design and implement a neural network in Python to predict the price of a house given a set of features. The function should return the trained model. Given the input features, the function should compile and fit the model using mean squared error as the loss function and 'adam' as the optimizer.
  assert type(design_and_implement_nn([0.8, 0.4, 0.7])) == keras.models.Sequential
  assert type(design_and_implement_nn([0.1, 0.2, 0.3])) == keras.models.Sequential
  assert type(design_and_implement_nn([1.0, 0.5, 0.9])) == keras.models.Sequential
  assert type(design_and_implement_nn([0.3, 0.7, 0.2])) == keras.models.Sequential
  assert type(design_and_implement_nn([])) == keras.models.Sequential
output: def design_and_implement_nn(features):
      import tensorflow as tf
      from tensorflow.keras.models import Sequential
      from tensorflow.keras.layers import Dense
      
      model = Sequential()
      model.add(Dense(10, input_dim=len(features), activation='relu'))
      model.add(Dense(1))
      
      model.compile(loss='mean_squared_error', optimizer='adam')
      
      X = tf.constant([features])
      y = tf.constant([0.0])  # Dummy target for fitting
      
      model.fit(X, y, epochs=1, verbose=0)
      
      return model