
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 a number from a hat containing the numbers $1$ to $50$, both without replacement. If Alice cannot determine who has the larger number, and Bob can still determine who has the larger number after hearing Alice's statement, and Bob's number is prime, andAlice multiplies Bob's number by $150$ and adds her own number to get a perfect square, find the sum of the two numbers drawn from the hat.

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