
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 $$\tan \alpha + \frac{1}{\tan \alpha} = \frac{5}{2}$$, find the value of $$2\sin^2(3\pi-\alpha) - 3\cos\left(\frac{\pi}{2}+\alpha\right)\sin\left(\frac{3\pi}{2}-\alpha\right) + 2$$.

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