
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
Alice and Bob each draw one number from a hat containing the numbers 1 to 50, without replacement. Given that Alice states she can't tell who has the larger number, and then Bob declares he knows who has the larger number, and he reveals his number is prime, and that if Alice multiplies Bob's number by 130 and adds her number, the result is a perfect square, calculate the sum of the two numbers drawn from the hat.

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