
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
Find \( \frac{a_1^3}{1 - 3a_1 + 3a_1^2} + \frac{a_2^3}{1 - 3a_2 + 3a_2^2} + \cdots + \frac{a_{101}^3}{1 - 3a_{101} + 3a_{101}^2} \), where \( a_n = \frac{n}{101} \).

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