
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
Given the line $3x+4y-15=0$ intersects with circle $O$: $x^{2}+y^{2}=25$ at points $A$ and $B$, and point $C$ is on circle $O$ with $S_{\triangle ABC}=8$, find the number of possible points $C$.

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