
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
Let $T$ be the set of lattice points in the coordinate plane, but this time both coordinates are integers between $1$ and $45$ inclusive. Exactly $700$ points in $T$ lie on or below a line with equation $y = mx$. The possible values of $m$ lie in an interval of length $\frac{c}{d}$, where $c$ and $d$ are relatively prime positive integers. What is $c+d?$
- **A)** $50$
- **B)** $75$
- **C)** $85$
- **D)** $100$
- **E)** $120$

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