
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 angles at which the following lines intersect:
1) The line \( x + y - 4 = 0 \) and the parabola \( 2y = 8 - x^2 \);
2) The ellipse \( x^2 + 4y^2 = 4 \) and the parabola \( 4y = 4 - 5x^2 \);
3) The sine curve \( y = \sin x \) and the cosine curve \( y = \cos x \).

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