
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 differentials of the functions:
1) \( y = x^3 \) at the point \( x = 0 \) if \(\Delta x = 0.3\)
2) \( y = x^3 - x^2 + 3x - 1 \)
3) \( r = \varphi^4 + 2^{\sin(3\varphi)} \)
4) \( y = \ln(x^2 + 1) + \arctan(\sqrt{x}) \) at the point \( x = 1 \) if \(\Delta x = 0.1\)

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