
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
Calculate the limits: 
a) $\lim _{x \rightarrow 1}\left(\frac{x}{x-1}-\frac{1}{\ln x}\right)$; 
b) $\lim _{x \rightarrow-\infty} x^{3} e^{x}$; 
c) $\lim _{x \rightarrow \pi / 2}(\cos x)^{(x-\pi / 2)}$; 
d) $\lim _{x \rightarrow 0}(1-\sin x)^{\operatorname{ctg}^{2} x}$.

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