
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 range where $4^{115}$ is between $3^{165}$ and $3^{166}$. How many pairs of integers $(x, y)$ are there such that $1 \leq x \leq 164$ and \[4^y < 3^x < 3^{x+2} < 4^{y+1}?\]
A) 158
B) 159
C) 160
D) 161
E) 162

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