
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 equations of two lines:

$$
A_{1} x + B_{1} y + C_{1} = 0 \quad \text{and} \quad A_{2} x + B_{2} y + C_{2} = 0
$$

a) Calculate the coordinates of the intersection point of these lines and the angle formed by them. Determine the conditions for these lines to be parallel and perpendicular.

b) By bringing the given equations to the normal form and using the result of the previous problem, derive the equations of the angle bisectors between these lines.

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