
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 how many positive integers \( n \) satisfy the condition:
\[ (150n)^{40} > n^{80} > 3^{160}. \]
**A)** 130
**B)** 135
**C)** 140
**D)** 145
**E)** 150

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