
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 \( R \) be a unit square region and \( n \geq 4 \) an integer. A point \( X \) in the interior of \( R \) is called \( n \)-ray partitional if there are \( n \) rays emanating from \( X \) that divide \( R \) into \( n \) triangles of equal area. How many points are \( 150 \)-ray partitional but not \( 90 \)-ray partitional?

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