
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
Given the line \( a x + b y + c = 0 \) where the coefficients \( a, b, \) and \( c \) are chosen from the set \( \{-3, -2, -1, 0, 1, 2, 3\} \) as 3 different elements, and the slope of the line forms an acute angle. Find the number of all such distinct lines.

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