
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
Given the set \( T = \{ 9^k \mid k \text{ is an integer}, 0 \leq k \leq 4000 \} \), and knowing that \( 9^{4000} \) has 3817 digits with its leftmost digit being 9, how many elements in \( T \) have 9 as their leftmost digit?

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