
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 the $xy$-coordinate plane, where both $x$ and $y$ are integers (lattice points). Determine the maximum possible value of $a$ such that the line does not pass through any lattice points for $0 < x \le 50$ and $\frac{1}{2} < m < a$.
A) $\frac{24}{49}$ 
B) $\frac{26}{51}$ 
C) $\frac{25}{50}$ 
D) $\frac{25}{49}$

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