
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
Determine how many pairs of integers $(m,n)$ are there such that $1\leq m\leq 2044$ and $$5^n < 2^m < 2^{m+1} < 5^{n+1}?$$ given that $5^{900}$ is between $2^{2100}$ and $2^{2101}$.
A) 899
B) 900
C) 901
D) 902

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