
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, with both coordinates being integers between 1 and 20, inclusive. A specific line y = mx results in exactly 200 points in T lying on or below this line. Find the length of the interval of possible values of m.

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