
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
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The three-digit integers from 100 to 500 are written consecutively to form the integer \(N=100101102\cdots498499500\). Suppose that \(3^k\) is the highest power of 3 that is a factor of \(N\). What is \(k\)?

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A) 2
B) 3
C) 4
D) 5
E) More than 5

**

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