
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
Calculate how many pairs of integers $(m, n)$ are there such that $1 \leq m \leq 1000$ and 
\[3^n < 2^m < 2^{m+1} < 3^{n+1}\].
A) 498
B) 499
C) 500
D) 501
E) 502

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