input: 
  def train_mnist_model():
      """
      Train a neural network model using TensorFlow to classify hand-written digits from the MNIST dataset.
      The model uses a two-layer fully connected neural network with ReLU activations and is trained using the Adam optimizer.
      
      Example:
      train_mnist_model()
      Output:
      Epoch: 0001 cost= 102.734565471
      Epoch: 0002 cost= 30.123456789
      ...
      Optimization Finished!
      Accuracy: 0.9456
      """
  
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(-1, 28*28).astype('float32') / 255
      x_test = x_test.reshape(-1, 28*28).astype('float32') / 255
      y_train = to_categorical(y_train, 10)
      y_test = to_categorical(y_test, 10)
  
      # Build the model
      model = models.Sequential([
          layers.Dense(512, 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
      history = model.fit(x_train, y_train, epochs=10, batch_size=128, validation_split=0.2)
  
      # Evaluate the model
      test_loss, test_acc = model.evaluate(x_test, y_test)
      print(f'Optimization Finished!\nAccuracy: {test_acc:.4f}')
  