
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 following limits:
a.) $\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}$.
b.) $\lim _{x \rightarrow \pi} \frac{\sin 3 x}{x-\pi}$.
c.) $\lim _{x \rightarrow 1} \frac{\cos \frac{\pi x}{2}}{x-1}$.
d.) $\lim _{x \rightarrow 0} \frac{1}{x} \sin \frac{\pi}{1+\pi x}$.

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