
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 line $y = mx + 3$ on a coordinate system. We seek the conditions on $m$ such that this line passes through no lattice points where $0 < x \leq 150$, for all $m$ satisfying $0.5 < m < b$. What is the largest possible value of $b$?
A) $\frac{75}{150}$
B) $\frac{75}{149}$
C) $\frac{76}{151}$
D) $\frac{77}{152}$

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