
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
Passing through the origin of the coordinate plane are  $180$  lines, including the coordinate axes,
which form  $1$  degree angles with one another at the origin. Determine the sum of the x-coordinates
of the points of intersection of these lines with the line  $y = 100-x$ 

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