
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 \( 7^{1234} \) is between \( 3^{2399} \) and \( 3^{2400} \). How many pairs of integers \( (m, n) \) are there such that \( 1 \leq m \leq 2398 \) and
\[ 7^n < 3^m < 3^{m+1} < 7^{n+1}? \]
A) 2466
B) 2467
C) 2468
D) 2469
E) 2470

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