
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 specified order for the given functions:

1) \( y = x^{3} + 2x^{2} - 4x + 1 \); \( y^{\prime \prime \prime} \) = ?

2) \( y = \ln x \); \( y^{(4)} \) = ?

3) \( s = t^{2} - t + 1 \); \( s^{\prime \prime}(0) \) = ?

4) \( f(x) = \sin 2x \); \( f^{(5)}\left(\frac{\pi}{2}\right) \) = ?

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