
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
In a plane Cartesian coordinate system, the vertices of square $OABC$ are $O(0,0)$, $A(100,0)$, $B(100,100)$, and $C(0,100)$. A grid point $P$ inside square $OABC$ (excluding the boundary and vertices) is called a "good point" if it satisfies the condition $S_{\triangle POA} \times S_{\triangle PBC} = S_{\triangle PAB} \times S_{\triangle POC}$. How many "good points" are there inside square $OABC$?

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