
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
Sofia wrote 3 different numbers on each side of 3 cards and laid the cards on a table in the following manner: The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. On the visible sides of the cards, the numbers are 17, 26, and 41 respectively. What is the sum of the hidden prime numbers?

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