
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
There are three two-digit numbers $A$, $B$, and $C$. 

- $A$ is a perfect square, and each of its digits is also a perfect square.
- $B$ is a prime number, and each of its digits is also a prime number, and their sum is also a prime number. 
- $C$ is a composite number, and each of its digits is also a composite number, the difference between its two digits is also a composite number. Furthermore, $C$ is between $A$ and $B$.

What is the sum of these three numbers $A$, $B$, and $C$?


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