
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 \( T = \{3^k | k \in \mathbb{Z}, 0 \le k \le 1500 \} \). Given that \( 3^{1500} = 3691 \cdots 2743 \) has \( 717 \) digits, how many elements of \( T \) begin with the digit \( 1 \)?

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