
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
Determine the value of the infinite product $(3^{1/2})(9^{1/4})(27^{1/8})(81^{1/16}) \dotsm.$ Enter your answer in the form "\sqrt[a]{b}", which represents $\sqrt[a]{b}.$

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