
    Design a feedback mechanism for a math learning system that helps students understand number patterns by finding the next number that reads the same forwards and backwards (palindrome) after their submitted answer. The system should take the student's numerical answer and identify the next palindromic number that is larger than their input, helping reinforce concepts of numerical symmetry and pattern recognition.
    

    
import sys

def next_smallest_palindrome(num):
    """
    Design a feedback mechanism for a math learning system that helps students understand number patterns by finding the next number that reads the same forwards and backwards (palindrome) after their submitted answer. The system should take the student's numerical answer and identify the next palindromic number that is larger than their input, helping reinforce concepts of numerical symmetry and pattern recognition.
    

    """
import sys

def next_smallest_palindrome(num):
    """
    Design a feedback mechanism for a math learning system that helps students understand number patterns by finding the next number that reads the same forwards and backwards (palindrome) after their submitted answer. The system should take the student's numerical answer and identify the next palindromic number that is larger than their input, helping reinforce concepts of numerical symmetry and pattern recognition.
    

    """
    numstr = str(num)
    for i in range(num + 1, sys.maxsize):
        if str(i) == str(i)[::-1]:
            return i