
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) \( y = x^3 - 3^x \);
2) \( F(\varphi) = \cos \frac{\varphi}{3} + \sin \frac{3}{\varphi} \);
3) \( z = \ln \left(1 + e^{10x}\right) + \operatorname{arcctg} e^{5x} \); calculate \(\left.dz\right|_{x=0; dx=0.1}\).

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