
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
Simplify \(\left(\frac{1 \times 3 \times 9 + 2 \times 6 \times 18 + \cdots + n \times 3n \times 9n}{1 \times 5 \times 25 + 2 \times 10 \times 50 + \cdots + n \times 5n \times 25n}\right)^{\frac{1}{3}}\).

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