
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
On a circle, 15 white points and 1 black point are marked. Consider all possible (convex) polygons with their vertices at these points.

We will classify them into two types:

- Type 1: those with only white vertices.
- Type 2: those with the black point as one of the vertices.

Are there more polygons of Type 1 or Type 2? How many more are there?

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