
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 derivative of the following functions:

1. $y=\sqrt[5]{x^{3}};$

2. $y=\dfrac{1}{x^{4}};$

3. $y=-2\sin \dfrac{x}{2}\left( 1-2\cos^{2}\dfrac{x}{4} \right);$ 

4. $y=\log _{2}x^{2}-\log _{2}x.$

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