
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  $T = \{9^k : k \ \text{is an integer}, 0 \le k \le 4000\}$ .  Given that  $9^{4000}$  has 3817 digits and that its first (leftmost) digit is 9, how many elements of  $T$  have 9 as their leftmost digit?

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