
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 derivatives of the following functions:
1) \( y^3 - 3y + 2ax = 0 \)
2) \( x^2 + 3xy + y^2 + 1 = 0 \). Compute \( y' \) at the point \( (2, -1) \)
3) \( \sin \varphi + r \varphi - 5r = 0 \). Compute \( \frac{dr}{d\psi} \)
4) \( e^y + xy = e \). Compute \( y' \) at the point \( (0, 1) \)

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