
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 unit square is divided into 9 equal parts by drawing two lines parallel to each side, and the middle part is removed. Each of the remaining 8 squares is again divided in the same manner into 9 parts, with the middle part again removed. Repeating this procedure \( n \) times, question:

1. How many squares with side length \( \frac{1}{3^{n}} \) remain?
2. What is the total area of the removed squares?

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