
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 the number of pairs of integers \( (m, n) \) such that \( 1 \leq m \leq 4024 \) and \[ 3^n < 2^m < 2^{m+1} < 3^{n+1}, \] given that \( 3^{1734} \) is between \( 2^{4023} \) and \( 2^{4024} \).
A) 1732
B) 1733
C) 1734
D) 1735
E) 1736

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