
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
Insert $n-2$ ($n\geqslant 3$) real numbers between $1$ and $16$ to form an increasing geometric sequence. If the product of these $n$ real numbers is denoted as $b\_n$, then $b\_3+b\_4+...+b\_n=$ \_\_\_\_\_\_.

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