
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 first two terms of a geometric progression are $4^{1/2}$ and $4^{1/3}$. The exponent in each subsequent term decreases by $1/6$ for the first two steps and then by $1/12$ thereafter. What is the fifth term of this geometric progression?

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