
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 \(3^{867}\) is between \(4^{1352}\) and \(4^{1353}\). How many pairs of integers \((m, n)\) are there such that \(1 \leq m \leq 1351\) and \(3^n < 4^m < 4^{m+1} < 3^{n+1}\)?

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