
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 integers \(5^{1234}\) falling between \(2^{2876}\) and \(2^{2878}\). Determine the number of integer pairs \((m,n)\) such that \(1 \leq m \leq 2875\) and \[5^n < 2^m < 2^{m+1} < 5^{n+1}.\]
**A)** 1232
**B)** 1233
**C)** 1234
**D)** 1235
**E)** 1236

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