
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 $T = \{7^k : k ~ \mbox{is an integer}, 0 \le k \le 3000\}$. Given that $7^{3000}$ results in a number with 2838 digits, and its first (leftmost) digit is 7, determine how many elements in $T$ have 7 as their leftmost digit.

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