
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
Gauss and his classmates were punished for being naughty at school, and the teacher assigned them a math problem:
From the natural numbers 1 to 100, two adjacent odd numbers are removed. The average of the remaining numbers is 51. What is the product of the two odd numbers that were removed?
Whoever gets the correct answer can go home. Gauss quickly gave the correct answer again.

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