
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 $y = mx + 3$ in an $xy$-coordinate system, where lattice points are points $(x, y)$ with integer coordinates. Determine the smallest value of $b$ such that the line does not pass through any lattice points for $0 < x \leq 150$ and $\frac{1}{3} < m < b$.
A) $\frac{51}{150}$
B) $\frac{52}{151}$
C) $\frac{53}{150}$
D) $\frac{51}{149}$
E) $\frac{52}{149}$

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