
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
Given that Alice says all the numbers in the set {1, 2, 3, ..., 500}, except she skips the middle number in each consecutive group of three numbers, Barbara says all the numbers that Alice doesn't say, except she also skips the middle number in each consecutive group of three numbers, Candice says all the numbers that neither Alice nor Barbara says, except she also skips the middle number in each consecutive group of three numbers, Debbie says all the numbers that none of the students with the first names beginning before hers in the alphabet say, except each also skips the middle number in each of her consecutive groups of three numbers, and Greg says all the numbers that none of the students with the first names beginning before his in the alphabet say, except each also skips the middle number in each of her consecutive groups of three numbers, and Hannah says the only number that no one else says, determine the number that Hannah says.

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