
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
Consider the following sequence of pieces, in which piece number 1 is a small square.

(a) How many small squares make up piece number 50?

(b) How many small squares are there in the union of pieces numbered 1 to 50?

(c) Observing the result from part (b), calculate
$$
2+4+6+\ldots+96+98+100
$$

(d) Calculate
$$
1+2+3+4+\ldots+97+98+99+100
$$

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