
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 \( T = \left\{9^{k} \mid k \right. \) be integers, \(\left.0 \leqslant k \leqslant 4000\right\} \). Given that \(9^{4000}\) has 3817 digits and its most significant digit is 9, how many elements in \(T\) have 9 as their most significant digit?
(The 8th American Mathematics Invitational, 1990)

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