
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
The common ratio of the geometric progression is $\frac{\sqrt[6]{2}}{\sqrt[4]{2}}=\frac{\sqrt[12]{2}}{\sqrt[6]{2}}$, so a general term of the sequence is $(\sqrt[4]{2})\left(\frac{\sqrt[6]{2}}{\sqrt[4]{2}}\right)^{n-1}=(\sqrt[4]{2})\left(\sqrt[12]{2}\right)^{2n-3}=\sqrt[4]{2}\cdot 2^{(2n-3)/12}=\sqrt[4]{2}\cdot 2^{n-3/4}$, so find the fourth term

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