input: 
  import numpy as np
  import keras
  from keras.layers import Dense, Conv2D, MaxPooling2D, Dropout, Flatten
  from keras.models import Sequential
  from keras.preprocessing.image import ImageDataGenerator
  
  def distinguish_cats_and_dogs_model() -> Sequential:
      """
      Create and compile a machine learning model using Keras that distinguishes between cats and dogs.
      The model consists of convolutional neural networks and is compiled with the Adam optimizer and binary crossentropy loss.
      The model is then trained on a dataset of 800 images of cats and dogs.
      
      Example:
      model = distinguish_cats_and_dogs_model()
      """
  
      # Create the neural network model
      model = Sequential()
  
      # Input layer
      model.add(Conv2D(32, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))
  
      # Hidden layers
      model.add(MaxPooling2D(pool_size = (2, 2)))
      model.add(Dropout(0.3))
      model.add(Conv2D(64, (3, 3), activation = 'relu'))
      model.add(MaxPooling2D(pool_size = (2, 2)))
      model.add(Dropout(0.3))
      model.add(Conv2D(64, (3, 3), activation = 'relu'))
      model.add(MaxPooling2D(pool_size = (2, 2)))
      model.add(Dropout(0.3))
  
      # Output layer
      model.add(Flatten())
      model.add(Dense(units = 128, activation = 'relu'))
      model.add(Dense(units = 1, activation = 'sigmoid'))
  
      # Compile the model
      model.compile(loss = 'binary_crossentropy', optimizer = 'adam', metrics = ['accuracy'])
  
      # Create data generator
      datagen = ImageDataGenerator(rescale = 1./255, shear_range = 0.2, zoom_range = 0.2, horizontal_flip = True)
  
      # Fit the model
      train_generator = datagen.flow_from_directory(directory = '/path/to/dataset', target_size = (64, 64), color_mode = 'rgb', class_mode = 'binary', batch_size = 32)
      model.fit_generator(generator = train_generator, steps_per_epoch = 800, epochs = 5, validation_data = test_generator, validation_steps = 200)
      
      return model
  
output:     return model