
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
Tasha and Amy both pick a number, and they notice that Tasha's number is greater than Amy's number by  12 . They each square their numbers to get a new number and see that the sum of these new numbers is half of  169 . Finally, they square their new numbers and note that Tasha's latest number is now greater than Amy's by  5070 . What is the sum of their original numbers?

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