
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
An integer \( N \) is selected at random from the range \( 1 \leq N \leq 2000 \). What is the probability that the remainder when \( N^{16} \) is divided by \( 6 \) is \( 1 \)?
A) \( \frac{1}{6} \)
B) \( \frac{1}{4} \)
C) \( \frac{1}{3} \)
D) \( \frac{1}{2} \)
E) \( \frac{2}{3} \)

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