
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 $\tan 2\_\theta= \frac{3}{4}\left(\pi < \theta < \frac{3\pi}{2}\right)$, find the value of $\frac{2{\cos }^{2} \frac{\theta}{2}+\sin \theta-1}{ \sqrt{2}\cos \left(\theta+ \frac{\pi}{4}\right)}$.

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