
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
Jaime loves to sum sequences of consecutive integers.

a) What result does Jaime get when he adds the first 2,019 positive integers?

b) Jaime adds 100 consecutive numbers and gets 17,050. What is the smallest number in this sequence?

c) Summing 180 numbers in sequence, Jaime gets 3,690. What is the smallest of these numbers?

d) Jaime added 100 consecutive positive numbers, but made a mistake by substituting one of them with its square, thus obtaining 7,500. Which number was squared?

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