
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
A unit-length segment is divided into 3 equal parts, and the middle part is discarded. Each of the remaining two segments is then divided into 3 equal parts, and their middle parts are also discarded. This process is repeated for the remaining segments, and so on. Suppose this process is repeated 16 times. How many segments of length $1 / 3^{16}$ remain?

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