
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
Charlie wrote down 6 different numbers on 3 different cards, with one number on each side of the card. The sums of the numbers on each card are the same. On the visible sides of the cards, the numbers are 81, 52, and 47. If the numbers on the hidden sides are all prime, calculate the average of the numbers on the hidden sides.

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