
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
Each lattice point in the coordinate plane centers a circle of radius $\frac{1}{5}$ and a square with side length $\frac{2}{5}$ whose sides are parallel to the coordinate axes. The line segment from $(0,0)$ to $(703, 299)$ intersects $m$ of the squares and $n$ of the circles. Find $m + n$.

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