
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 \(5^{1250} < 2^{2900} < 2^{2901}\). Determine how many pairs of integers $(m,n)$ exist such that \(1 \leq m \leq 2899\) and
\[
5^n < 2^m < 2^{m+3} < 5^{n+1}.
\]
A) 275
B) 279
C) 280
D) 281
E) 282

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