
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 given function and then evaluate it at the specified value of the argument:

1) \( F(x)=\frac{(1-\sqrt{x})^{2}}{x}, \quad x=0.01 \)
2) \( z=\frac{\cos t}{1-\sin t}, \quad t=\frac{\pi}{6} \)
3) \( y=\frac{a+b}{3-2 x}+\frac{5 x^{4}-1}{a-b}, \quad x=0 \)

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