
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
We are looking for a five-digit number with the following properties: it is a palindrome (i.e., it reads the same forward and backward), it is divisible by twelve, and it contains the digit 2 immediately after the digit 4 in its representation. Determine all possible numbers that satisfy the given conditions.

Present the answer in LaTex format: \boxed{Your answer}
user