
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 with 35 sides has 5 vertices which do not form diagonals due to specific restrictions (e.g., barrier points that block connections). How many diagonals does this polygon have with the given conditions?

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