
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
Given a large data $3^{2000}$, which can be represented in scientific notation as $m \times 10^{n}$, where $m \in (1,10)$, $n \in N^{*}$, and knowing $0.4771 \lt \lg 3 \lt 0.4772$, calculate the value of n.

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