
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
Using differentiation formulas, find the derivatives of the following functions:
1) \( y = x^{2} - 5x + 4 \)
2) \( y = \sqrt{x} + \frac{5}{\sqrt[3]{x}} - \frac{1}{x^{2}} + \frac{1}{3x^{3}} \)
3) \( z = x^{5} \left( 2 - \frac{x}{3} + 3x^{2} \right) \)
4) \( f(x) = \frac{x^{2}}{x^{2} + 1} \)
5) \( \varphi(t) = \frac{10}{a \sin t - b \cos t} \)
6) \( R(a) = \frac{\cos \alpha \operatorname{ctg} \alpha}{1 + 2 \operatorname{tg} c} \)

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