
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
A lattice point in an $xy$-coordinate system is any point $(x, y)$ where both $x$ and $y$ are integers. The graph of $y = mx + 3$ passes through no lattice point with $0 < x \leq 150$ for all $m$ such that $\frac{2}{3} < m < a$. What is the maximum possible value of $a$?
A) $\frac{151}{150}$
B) $\frac{151}{147}$
C) $\frac{152}{151}$
D) $\frac{153}{152}$
E) $\frac{2}{3}$

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