
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
Given that the first term of a geometric sequence $\{a\_n\}$ is $2$, and the common ratio is $2$, find the value of $\frac{a_{a_{n+1}}}{a_{a_1} \cdot a_{a_2} \cdot a_{a_3} \cdot \, …a_{a_n}} = \_\_\_\_\_\_.$

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