
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
Two circles, each with a radius of 5 units, are drawn in the coordinate plane such that their centers \(A\) and \(C\) have coordinates \((0,0)\) and \((8,0)\) respectively. How many points where both coordinates are integers lie within the intersection of these circles (including its boundary)?

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