
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
Let \( R = \{ 8^k : k \text{ is an integer}, 0 \leq k \leq 2000 \} \). It is given that \( 8^{2000} \) has 1909 digits and that its first (leftmost) digit is 8. Determine how many elements of \( R \) have 8 as their leftmost digit.

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