
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
Find the angle between two lines:

1) \( y = -2x \) and \( y = 3x + 5 \)

2) \( 4x + 2y - 5 = 0 \) and \( 6x + 3y + 1 = 0 \)

3) \( V \overline{3}x - y - 2 = 0 \) and \( \sqrt{3x} + y - 1 = 0 \)

4) \( 2x + 3y - 1 = 0 \) and \( 3x - 2y + 1 = 0 \)

5) \( 3x + 4y - 5 = 0 \) and \( 5x - 2y + 7 = 0 \)

6) \( y = 2x + 3 \) and \( y - 4 = 0 \)

7) \( 2x - 4y + 7 = 0 \) and \( x - 5 = 0 \)

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