input: 
  def neural_network_brain() -> str:
      """ Create and train a TensorFlow-based neural network model for classifying hand-written digits from the MNIST dataset.
      The network should have two hidden layers, each with 256 neurons, and use Adam optimizer for training.
      The function should return the accuracy of the model after training.
      
      Example:
      for neural_network_brain() == "Accuracy: 0.9521"
      """
  
output:     import tensorflow as tf
      from tensorflow.keras import layers, models
      from tensorflow.keras.datasets import mnist
      from tensorflow.keras.utils import to_categorical
  
      # Load and preprocess the MNIST dataset
      (x_train, y_train), (x_test, y_test) = mnist.load_data()
      x_train = x_train.reshape((x_train.shape[0], 28 * 28)).astype('float32') / 255
      x_test = x_test.reshape((x_test.shape[0], 28 * 28)).astype('float32') / 255
      y_train = to_categorical(y_train)
      y_test = to_categorical(y_test)
  
      # Build the neural network model
      model = models.Sequential([
          layers.Dense(256, activation='relu', input_shape=(28 * 28,)),
          layers.Dense(256, activation='relu'),
          layers.Dense(10, activation='softmax')
      ])
  
      # Compile the model
      model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])
  
      # Train the model
      model.fit(x_train, y_train, epochs=5, batch_size=128, validation_split=0.2)
  
      # Evaluate the model
      test_loss, test_acc = model.evaluate(x_test, y_test)
  
      return f"Accuracy: {test_acc:.4f}"