
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 $7^{1233}$ is between $3^{2888}$ and $3^{2889}$. How many pairs of integers $(m,n)$ are there such that $1 \leq m \leq 2887$ and \[7^n < 3^m < 3^{m+3} < 7^{n+1}?\]
A) 2464
B) 2465
C) 2466
D) 2467
E) 2468

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