
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
Calculate the root

$$
\left(\frac{1 \cdot 2 \cdot 4+2 \cdot 4 \cdot 8+3 \cdot 6 \cdot 12+\ldots}{1 \cdot 3 \cdot 9+2 \cdot 6 \cdot 18+3 \cdot 9 \cdot 27+\ldots}\right)^{\frac{1}{3}}
$$

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