
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 $T = \{7^k \mid k \in \mathbb{Z}, 0 \leq k \leq 2011\}$. It is known that $7^{2011} = 1243 \cdots 7329$ has $1602$ digits. How many elements of $T$ begin with the digit $3$?

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