
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
From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, randomly select three different elements as the values of a, b, and c in the line l: ax + by + c = 0. Determine the number of lines l for which the slope angle is less than 135° and the x-intercept is less than -1.

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