
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
Given $\sin \left(\frac{3\pi }{2}+\theta \right)=\frac{1}{4}$,

find the value of $\frac{\cos (\pi +\theta )}{\cos \theta [\cos (\pi +\theta )-1]}+\frac{\cos (\theta -2\pi )}{\cos (\theta +2\pi )\cos (\theta +\pi )+\cos (-\theta )}$.

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