
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
There are 9 points on a plane, of which 4 points are on the same line, and any other three points are not collinear.

(1) How many triangles can be formed by taking every three points as vertices? ($($Answer with a number$)$)

(2) How many rays can be formed by taking one point as an endpoint and passing through another point? ($($Answer with a number$)$)

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