
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
(1) Calculate the following sequences and complete the blanks:
$$1+3=4$$
$$1+3+5=9$$
$$1+3+5+7=16$$
$$1+3+5+7+9=\ \ $$
...
(2) Carefully observe the aforementioned operations and results, and express the following sum using powers:
$$1+3+5+7+…+195+197+199=\ \ \ .$$
(3) Calculate:
$$101+103+105+107+…+195+197+199.$$

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