
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
Consider the inequality $5^n < 3^m < 3^{m+1} < 5^{n+1}$, where $1 \leq m \leq 3000$. Determine how many integer pairs $(m, n)$ satisfy this relationship.
A) 980
B) 990
C) 1000
D) 1010
E) 1020

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