
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 that angle $\alpha=-\frac{35}{6}\pi$, calculate the value of 
$$\frac{2\sin(\pi+\alpha)\cos(\pi-\alpha)-\sin\left(\frac{3\pi}{2}+\alpha\right)}{1+\sin^{2}\alpha-\cos\left(\frac{\pi}{2}+\alpha\right)-\cos^{2}(\pi+\alpha)}.$$

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