
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
The number \(5^{900}\) is between \(2^{2080}\) and \(2^{2081}\). How many pairs of integers \((m, n)\) are there such that \(1\leq m\leq 2140\) and 
\[5^n < 2^m < 2^{m+1} < 5^{n+1}?\]
A) 1238
B) 1239
C) 1240
D) 1241
E) 1242

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