
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
Let $S$ be a unit square region and $n \geq 3$ an integer. A point $Y$ inside $S$ is termed n-ray partitional if there are $n$ rays starting from $Y$ that divide $S$ into $n$ triangles of equal area. Identify how many points are $75$-ray partitional but not $45$-ray partitional.

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