
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 regular polygon of 12 sides is exactly enclosed by 12 regular polygons of \(n\) sides each, such that four polygons touch at each vertex of the 12-sided polygon without overlapping. What is the value of \( n \)?
- **A**. 6
- **B**. 10
- **C**. 12
- **D**. 15
- **E**. 18

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