
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 convex polygon has 25 sides. Each side has a unique intersection outside the polygon, forming additional vertices where the extensions of opposite sides meet. How many diagonals does this original convex polygon have, excluding any lines connecting these new intersection points?

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