
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
We want to attach a curtain to the rod. We can ensure equal distances easily if, after clipping the two outermost clips, there is a middle clip in the remaining portion. Moreover, we require that this condition holds for each further division, with a middle clip being placed after each subsequent division. How many clips can we attach to the curtain rod if we want to fix the curtain in this manner?

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