
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
On a rectangular geoboard with a configuration of 5x7 (5 rows, 7 columns), two points A and B are placed at (3,2) and (5,2), respectively. Consequently, point C is to be chosen from the remaining $33$ points. How many of these $33$ points will result in triangle ABC being isosceles?

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