
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
Evaluate (1·2·4 + 2·4·8 + 3·6·12 + 4·8·16 + ... + n·2n·4n)^(1/3) / (1·3·9 + 2·6·18 + 3·9·27 + 4·12·36 + ... + n·3n·9n)^(1/3).

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