
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 vertices of a regular dodecagon are $C_{1}, C_{2}, \ldots, C_{12}$. The vertices with even indices are connected to all other vertices. How many internal points do these diagonals intersect, and into how many parts does this dodecagon get divided?

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