
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
At each lattice point $(i, j)$ on the coordinate plane, there is a circle of radius $\frac{1}{8}$ and a square of side length $\frac{1}{4}$, with sides parallel to the coordinate axes. A line segment runs from $(0, 0)$ to $(2017, 917)$. Calculate the total number of different squares and circles that the line segment intersects.

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